%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP200^1 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 08:56:22 AM UTC 2026
% Result : Theorem 4.43s 2.45s
% Output : Refutation 4.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 14 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 22 ( 21 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 103 ( 16 ~; 3 |; 3 &; 79 @)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 52 ( 51 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 172 ( 170 usr; 9 con; 0-3 aty)
% Number of variables : 21 ( 0 ^; 21 !; 0 ?; 21 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
set_char: $tType ).
thf(type_def_6,type,
char: $tType ).
thf(type_def_7,type,
option_fml: $tType ).
thf(type_def_9,type,
set_Pr927595527on_fml: $tType ).
thf(type_def_10,type,
option_game: $tType ).
thf(type_def_11,type,
set_Pr622314946on_fml: $tType ).
thf(type_def_12,type,
option_trm: $tType ).
thf(type_def_13,type,
set_Pr1471344007on_trm: $tType ).
thf(type_def_14,type,
set_variable: $tType ).
thf(type_def_15,type,
trm: $tType ).
thf(type_def_16,type,
set_Pr1235432374le_trm: $tType ).
thf(type_def_17,type,
set_Pr943832262on_trm: $tType ).
thf(type_def_18,type,
variable: $tType ).
thf(type_def_19,type,
real: $tType ).
thf(type_def_20,type,
fml: $tType ).
thf(type_def_21,type,
game: $tType ).
thf(type_def_22,type,
produc1072747943on_trm: $tType ).
thf(type_def_23,type,
produc464795408on_trm: $tType ).
thf(type_def_24,type,
produc1024976764on_trm: $tType ).
thf(type_def_25,type,
denotational_interp: $tType ).
thf(type_def_26,type,
produc833882726rp_trm: $tType ).
thf(type_def_27,type,
produc46605351on_fml: $tType ).
thf(type_def_28,type,
produc1810527345on_trm: $tType ).
thf(type_def_29,type,
produc1739631244on_fml: $tType ).
thf(type_def_30,type,
produc1016592119n_game: $tType ).
thf(type_def_31,type,
produc1456309597on_fml: $tType ).
thf(type_def_32,type,
produc1418842292n_game: $tType ).
thf(type_def_33,type,
produc1367888000le_trm: $tType ).
thf(type_def_34,type,
produc1699626005le_trm: $tType ).
thf(type_def_35,type,
produc1872652007on_fml: $tType ).
thf(type_def_36,type,
produc1158546023on_trm: $tType ).
thf(type_def_37,type,
produc1928189433on_fml: $tType ).
thf(type_def_38,type,
produc591588199on_fml: $tType ).
thf(type_def_39,type,
produc2024965863on_trm: $tType ).
thf(type_def_40,type,
produc1279577057le_trm: $tType ).
thf(type_def_41,type,
produc2018724225on_trm: $tType ).
thf(type_def_42,type,
produc432717079riable: $tType ).
thf(type_def_43,type,
produc1593312387r_char: $tType ).
thf(type_def_44,type,
product_prod_trm_trm: $tType ).
thf(type_def_45,type,
produc1408538418on_fml: $tType ).
thf(type_def_46,type,
set_Pr1045337287on_fml: $tType ).
thf(type_def_47,type,
set_Pr1588097095on_trm: $tType ).
thf(type_def_48,type,
set_Pr1625152599n_game: $tType ).
thf(type_def_49,type,
set_Pr1918373977on_fml: $tType ).
thf(type_def_50,type,
set_Pr519625031on_fml: $tType ).
thf(type_def_51,type,
set_Pr1062384839on_trm: $tType ).
thf(type_def_52,type,
set_Pr181266295riable: $tType ).
thf(type_def_53,type,
set_Pr491793543rm_trm: $tType ).
thf(type_def_54,type,
set_Pr1969262145le_trm: $tType ).
thf(type_def_55,type,
set_Pr604539619r_char: $tType ).
thf(type_def_56,type,
set_Pr1481565921on_trm: $tType ).
thf(func_def_0,type,
produc1699626005le_trm: $tType ).
thf(func_def_1,type,
produc1418842292n_game: $tType ).
thf(func_def_2,type,
set_Pr1918373977on_fml: $tType ).
thf(func_def_3,type,
set_Pr1062384839on_trm: $tType ).
thf(func_def_4,type,
set_Pr519625031on_fml: $tType ).
thf(func_def_5,type,
set_Pr1588097095on_trm: $tType ).
thf(func_def_6,type,
set_Pr1045337287on_fml: $tType ).
thf(func_def_7,type,
produc1928189433on_fml: $tType ).
thf(func_def_8,type,
produc2024965863on_trm: $tType ).
thf(func_def_9,type,
produc591588199on_fml: $tType ).
thf(func_def_10,type,
produc1158546023on_trm: $tType ).
thf(func_def_11,type,
produc1872652007on_fml: $tType ).
thf(func_def_12,type,
set_Pr1481565921on_trm: $tType ).
thf(func_def_13,type,
set_Pr1969262145le_trm: $tType ).
thf(func_def_14,type,
produc2018724225on_trm: $tType ).
thf(func_def_15,type,
produc1279577057le_trm: $tType ).
thf(func_def_16,type,
set_Pr1625152599n_game: $tType ).
thf(func_def_17,type,
set_Pr622314946on_fml: $tType ).
thf(func_def_18,type,
set_Pr1471344007on_trm: $tType ).
thf(func_def_19,type,
set_Pr927595527on_fml: $tType ).
thf(func_def_20,type,
set_Pr181266295riable: $tType ).
thf(func_def_21,type,
produc1016592119n_game: $tType ).
thf(func_def_22,type,
produc1739631244on_fml: $tType ).
thf(func_def_23,type,
produc1072747943on_trm: $tType ).
thf(func_def_24,type,
produc1456309597on_fml: $tType ).
thf(func_def_25,type,
produc1810527345on_trm: $tType ).
thf(func_def_26,type,
produc46605351on_fml: $tType ).
thf(func_def_27,type,
produc432717079riable: $tType ).
thf(func_def_28,type,
set_Pr943832262on_trm: $tType ).
thf(func_def_29,type,
set_Pr1235432374le_trm: $tType ).
thf(func_def_30,type,
produc1024976764on_trm: $tType ).
thf(func_def_31,type,
produc1408538418on_fml: $tType ).
thf(func_def_32,type,
produc464795408on_trm: $tType ).
thf(func_def_33,type,
produc833882726rp_trm: $tType ).
thf(func_def_34,type,
produc1367888000le_trm: $tType ).
thf(func_def_35,type,
set_Pr604539619r_char: $tType ).
thf(func_def_36,type,
set_Pr491793543rm_trm: $tType ).
thf(func_def_37,type,
produc1593312387r_char: $tType ).
thf(func_def_38,type,
product_prod_trm_trm: $tType ).
thf(func_def_39,type,
option_game: $tType ).
thf(func_def_40,type,
option_trm: $tType ).
thf(func_def_41,type,
option_fml: $tType ).
thf(func_def_42,type,
denotational_interp: $tType ).
thf(func_def_43,type,
set_variable: $tType ).
thf(func_def_44,type,
set_char: $tType ).
thf(func_def_45,type,
variable: $tType ).
thf(func_def_46,type,
game: $tType ).
thf(func_def_47,type,
char: $tType ).
thf(func_def_48,type,
trm: $tType ).
thf(func_def_49,type,
fml: $tType ).
thf(func_def_50,type,
real: $tType ).
thf(func_def_51,type,
bNF_Gr1866170027on_fml: set_char > ( char > option_fml ) > ( char > option_fml ) > set_Pr927595527on_fml ).
thf(func_def_52,type,
bNF_Gr756940202on_fml: set_char > ( char > option_game ) > ( char > option_fml ) > set_Pr622314946on_fml ).
thf(func_def_53,type,
bNF_Gr1666135339on_trm: set_char > ( char > option_trm ) > ( char > option_trm ) > set_Pr1471344007on_trm ).
thf(func_def_54,type,
bNF_Gr852774302le_trm: set_char > ( char > set_variable ) > ( char > trm ) > set_Pr1235432374le_trm ).
thf(func_def_55,type,
bNF_Gr951178926on_trm: set_char > ( char > char ) > ( char > option_trm ) > set_Pr943832262on_trm ).
thf(func_def_56,type,
bNF_Gr600956991on_fml: set_variable > ( variable > option_fml ) > ( variable > option_fml ) > set_Pr927595527on_fml ).
thf(func_def_57,type,
bNF_Gr2142503190on_fml: set_variable > ( variable > option_game ) > ( variable > option_fml ) > set_Pr622314946on_fml ).
thf(func_def_58,type,
bNF_Gr400922303on_trm: set_variable > ( variable > option_trm ) > ( variable > option_trm ) > set_Pr1471344007on_trm ).
thf(func_def_59,type,
bNF_Gr1330108682le_trm: set_variable > ( variable > set_variable ) > ( variable > trm ) > set_Pr1235432374le_trm ).
thf(func_def_60,type,
bNF_Gr1933470746on_trm: set_variable > ( variable > char ) > ( variable > option_trm ) > set_Pr943832262on_trm ).
thf(func_def_61,type,
bNF_Gr806120164on_fml: set_Pr927595527on_fml > ( option_fml > option_fml ) > set_Pr927595527on_fml ).
thf(func_def_62,type,
denota1419872369iation: ( variable > real ) > ( variable > real ) > set_variable > $o ).
thf(func_def_63,type,
none_fml: option_fml ).
thf(func_def_64,type,
none_game: option_game ).
thf(func_def_65,type,
none_trm: option_trm ).
thf(func_def_66,type,
some_fml: fml > option_fml ).
thf(func_def_67,type,
some_game: game > option_game ).
thf(func_def_68,type,
some_trm: trm > option_trm ).
thf(func_def_69,type,
case_option_o_fml: $o > ( fml > $o ) > option_fml > $o ).
thf(func_def_70,type,
case_option_o_game: $o > ( game > $o ) > option_game > $o ).
thf(func_def_71,type,
case_option_o_trm: $o > ( trm > $o ) > option_trm > $o ).
thf(func_def_72,type,
the_fml: option_fml > fml ).
thf(func_def_73,type,
the_game: option_game > game ).
thf(func_def_74,type,
the_trm: option_trm > trm ).
thf(func_def_75,type,
ord_le802833166_fml_o: ( option_fml > option_fml > $o ) > ( option_fml > option_fml > $o ) > $o ).
thf(func_def_76,type,
ord_le181580155_fml_o: ( option_fml > $o ) > ( option_fml > $o ) > $o ).
thf(func_def_77,type,
ord_le1588489637_fml_o: ( option_game > option_fml > $o ) > ( option_game > option_fml > $o ) > $o ).
thf(func_def_78,type,
ord_le847028878_trm_o: ( option_trm > option_trm > $o ) > ( option_trm > option_trm > $o ) > $o ).
thf(func_def_79,type,
ord_le1957133745_trm_o: ( option_trm > $o ) > ( option_trm > $o ) > $o ).
thf(func_def_80,type,
ord_le90123726_trm_o: ( produc1072747943on_trm > produc1072747943on_trm > $o ) > ( produc1072747943on_trm > produc1072747943on_trm > $o ) > $o ).
thf(func_def_81,type,
ord_le1721128566_trm_o: ( produc1072747943on_trm > $o ) > ( produc1072747943on_trm > $o ) > $o ).
thf(func_def_82,type,
ord_le157637894_trm_o: ( produc464795408on_trm > produc464795408on_trm > $o ) > ( produc464795408on_trm > produc464795408on_trm > $o ) > $o ).
thf(func_def_83,type,
ord_le1222882015_trm_o: ( produc464795408on_trm > $o ) > ( produc464795408on_trm > $o ) > $o ).
thf(func_def_84,type,
ord_le370603054_trm_o: ( produc1024976764on_trm > produc1024976764on_trm > $o ) > ( produc1024976764on_trm > produc1024976764on_trm > $o ) > $o ).
thf(func_def_85,type,
ord_le373274227_trm_o: ( produc1024976764on_trm > $o ) > ( produc1024976764on_trm > $o ) > $o ).
thf(func_def_86,type,
ord_le691957041_trm_o: ( set_variable > trm > $o ) > ( set_variable > trm > $o ) > $o ).
thf(func_def_87,type,
ord_le1890124833_trm_o: ( char > option_trm > $o ) > ( char > option_trm > $o ) > $o ).
thf(func_def_88,type,
ord_less_eq_char_o: ( char > $o ) > ( char > $o ) > $o ).
thf(func_def_89,type,
ord_le1407353162able_o: ( variable > $o ) > ( variable > $o ) > $o ).
thf(func_def_90,type,
ord_le778974119on_fml: set_Pr927595527on_fml > set_Pr927595527on_fml > $o ).
thf(func_def_91,type,
ord_le782333474on_fml: set_Pr622314946on_fml > set_Pr622314946on_fml > $o ).
thf(func_def_92,type,
ord_le1322722599on_trm: set_Pr1471344007on_trm > set_Pr1471344007on_trm > $o ).
thf(func_def_93,type,
ord_le2102862870le_trm: set_Pr1235432374le_trm > set_Pr1235432374le_trm > $o ).
thf(func_def_94,type,
ord_le541293862on_trm: set_Pr943832262on_trm > set_Pr943832262on_trm > $o ).
thf(func_def_95,type,
ord_less_eq_set_char: set_char > set_char > $o ).
thf(func_def_96,type,
ord_le282106107riable: set_variable > set_variable > $o ).
thf(func_def_97,type,
order_272405634riable: ( set_variable > $o ) > set_variable ).
thf(func_def_98,type,
produc1132922070rp_trm: denotational_interp > trm > produc833882726rp_trm ).
thf(func_def_99,type,
produc909629463on_fml: option_fml > option_fml > produc46605351on_fml ).
thf(func_def_100,type,
produc1447374177on_trm: option_fml > option_trm > produc1810527345on_trm ).
thf(func_def_101,type,
produc2124676926on_fml: option_game > option_fml > produc1739631244on_fml ).
thf(func_def_102,type,
produc1111617711n_game: option_game > option_game > produc1016592119n_game ).
thf(func_def_103,type,
produc171850061on_fml: option_trm > option_fml > produc1456309597on_fml ).
thf(func_def_104,type,
produc709594775on_trm: option_trm > option_trm > produc1072747943on_trm ).
thf(func_def_105,type,
produc2015636557le_trm: produc1418842292n_game > produc1367888000le_trm > produc1699626005le_trm ).
thf(func_def_106,type,
produc1367044951on_fml: produc46605351on_fml > produc46605351on_fml > produc1872652007on_fml ).
thf(func_def_107,type,
produc2132972503on_trm: produc1810527345on_trm > produc1810527345on_trm > produc1158546023on_trm ).
thf(func_def_108,type,
produc556056113on_fml: produc1739631244on_fml > produc1739631244on_fml > produc1928189433on_fml ).
thf(func_def_109,type,
produc1235825367on_fml: produc1456309597on_fml > produc1456309597on_fml > produc591588199on_fml ).
thf(func_def_110,type,
produc2001752919on_trm: produc1072747943on_trm > produc1072747943on_trm > produc2024965863on_trm ).
thf(func_def_111,type,
produc1056455193le_trm: produc1367888000le_trm > produc1367888000le_trm > produc1279577057le_trm ).
thf(func_def_112,type,
produc444919481on_trm: produc464795408on_trm > produc464795408on_trm > produc2018724225on_trm ).
thf(func_def_113,type,
produc1766592463riable: set_variable > set_variable > produc432717079riable ).
thf(func_def_114,type,
produc1482344242le_trm: set_variable > trm > produc1367888000le_trm ).
thf(func_def_115,type,
produc1500300866on_trm: char > option_trm > produc464795408on_trm ).
thf(func_def_116,type,
produc19545147r_char: char > char > produc1593312387r_char ).
thf(func_def_117,type,
product_Pair_trm_trm: trm > trm > product_prod_trm_trm ).
thf(func_def_118,type,
produc1205977188on_fml: variable > option_fml > produc1408538418on_fml ).
thf(func_def_119,type,
produc1743721902on_trm: variable > option_trm > produc1024976764on_trm ).
thf(func_def_120,type,
collec670974098on_fml: ( produc46605351on_fml > $o ) > set_Pr927595527on_fml ).
thf(func_def_121,type,
collec749447393on_fml: ( produc1739631244on_fml > $o ) > set_Pr622314946on_fml ).
thf(func_def_122,type,
collec1697116690on_trm: ( produc1072747943on_trm > $o ) > set_Pr1471344007on_trm ).
thf(func_def_123,type,
collec575343829le_trm: ( produc1367888000le_trm > $o ) > set_Pr1235432374le_trm ).
thf(func_def_124,type,
collec1756633317on_trm: ( produc464795408on_trm > $o ) > set_Pr943832262on_trm ).
thf(func_def_125,type,
collect_char: ( char > $o ) > set_char ).
thf(func_def_126,type,
collect_variable: ( variable > $o ) > set_variable ).
thf(func_def_127,type,
geq: trm > trm > fml ).
thf(func_def_128,type,
assign: variable > trm > game ).
thf(func_def_129,type,
ode: char > trm > game ).
thf(func_def_130,type,
test: fml > game ).
thf(func_def_131,type,
const: char > trm ).
thf(func_def_132,type,
differential: trm > trm ).
thf(func_def_133,type,
func: char > trm > trm ).
thf(func_def_134,type,
number: real > trm ).
thf(func_def_135,type,
plus: trm > trm > trm ).
thf(func_def_136,type,
times: trm > trm > trm ).
thf(func_def_137,type,
var: variable > trm ).
thf(func_def_138,type,
uSubst834381837ssigno: variable > option_trm > option_game ).
thf(func_def_139,type,
uSubst157155628no_rel: produc1024976764on_trm > produc1024976764on_trm > $o ).
thf(func_def_140,type,
uSubst716837505ntialo: option_trm > option_trm ).
thf(func_def_141,type,
uSubst2051024824lo_rel: option_trm > option_trm > $o ).
thf(func_def_142,type,
uSubst152838031e_Geqo: option_trm > option_trm > option_fml ).
thf(func_def_143,type,
uSubst1304144938qo_rel: produc1072747943on_trm > produc1072747943on_trm > $o ).
thf(func_def_144,type,
uSubst1827052306e_ODEo: char > option_trm > option_game ).
thf(func_def_145,type,
uSubst299938919Eo_rel: produc464795408on_trm > produc464795408on_trm > $o ).
thf(func_def_146,type,
uSubst141955042_Pluso: option_trm > option_trm > option_trm ).
thf(func_def_147,type,
uSubst691094423so_rel: produc1072747943on_trm > produc1072747943on_trm > $o ).
thf(func_def_148,type,
uSubst1367128042_Testo: option_fml > option_game ).
thf(func_def_149,type,
uSubst954181007to_rel: option_fml > option_fml > $o ).
thf(func_def_150,type,
uSubst918876924Timeso: option_trm > option_trm > option_trm ).
thf(func_def_151,type,
uSubst924844285so_rel: produc1072747943on_trm > produc1072747943on_trm > $o ).
thf(func_def_152,type,
uSubst1559070963pconst: produc1418842292n_game > set_variable > char > option_trm ).
thf(func_def_153,type,
uSubst516392804stappf: produc1418842292n_game > set_variable > fml > option_fml ).
thf(func_def_154,type,
uSubst516392818stappt: produc1418842292n_game > set_variable > trm > option_trm ).
thf(func_def_155,type,
uSubst1917534215pt_rel: produc1699626005le_trm > produc1699626005le_trm > $o ).
thf(func_def_156,type,
accp_option_fml: ( option_fml > option_fml > $o ) > option_fml > $o ).
thf(func_def_157,type,
accp_option_trm: ( option_trm > option_trm > $o ) > option_trm > $o ).
thf(func_def_158,type,
accp_P758790320on_trm: ( produc1072747943on_trm > produc1072747943on_trm > $o ) > produc1072747943on_trm > $o ).
thf(func_def_159,type,
accp_P1877119646le_trm: ( produc1699626005le_trm > produc1699626005le_trm > $o ) > produc1699626005le_trm > $o ).
thf(func_def_160,type,
accp_P419951815on_trm: ( produc464795408on_trm > produc464795408on_trm > $o ) > produc464795408on_trm > $o ).
thf(func_def_161,type,
accp_P394694195on_trm: ( produc1024976764on_trm > produc1024976764on_trm > $o ) > produc1024976764on_trm > $o ).
thf(func_def_162,type,
lex_pr314879023on_fml: set_Pr927595527on_fml > set_Pr927595527on_fml > set_Pr1045337287on_fml ).
thf(func_def_163,type,
lex_pr852623737on_trm: set_Pr927595527on_fml > set_Pr1471344007on_trm > set_Pr1588097095on_trm ).
thf(func_def_164,type,
lex_pr425996582on_fml: set_Pr1625152599n_game > set_Pr927595527on_fml > set_Pr1918373977on_fml ).
thf(func_def_165,type,
lex_pr1724583269on_fml: set_Pr1471344007on_trm > set_Pr927595527on_fml > set_Pr519625031on_fml ).
thf(func_def_166,type,
lex_pr114844335on_trm: set_Pr1471344007on_trm > set_Pr1471344007on_trm > set_Pr1062384839on_trm ).
thf(func_def_167,type,
lex_pr1522821402le_trm: set_Pr181266295riable > set_Pr491793543rm_trm > set_Pr1969262145le_trm ).
thf(func_def_168,type,
lex_pr1901327402on_trm: set_Pr604539619r_char > set_Pr1471344007on_trm > set_Pr1481565921on_trm ).
thf(func_def_169,type,
member1287158352on_fml: produc46605351on_fml > set_Pr927595527on_fml > $o ).
thf(func_def_170,type,
member1883102883on_fml: produc1739631244on_fml > set_Pr622314946on_fml > $o ).
thf(func_def_171,type,
member191809696n_game: produc1016592119n_game > set_Pr1625152599n_game > $o ).
thf(func_def_172,type,
member165817296on_trm: produc1072747943on_trm > set_Pr1471344007on_trm > $o ).
thf(func_def_173,type,
member450497296on_fml: produc1872652007on_fml > set_Pr1045337287on_fml > $o ).
thf(func_def_174,type,
member1883874960on_trm: produc1158546023on_trm > set_Pr1588097095on_trm > $o ).
thf(func_def_175,type,
member113767842on_fml: produc1928189433on_fml > set_Pr1918373977on_fml > $o ).
thf(func_def_176,type,
member1316917136on_fml: produc591588199on_fml > set_Pr519625031on_fml > $o ).
thf(func_def_177,type,
member602811152on_trm: produc2024965863on_trm > set_Pr1062384839on_trm > $o ).
thf(func_def_178,type,
member1150310282le_trm: produc1279577057le_trm > set_Pr1969262145le_trm > $o ).
thf(func_def_179,type,
member1950256170on_trm: produc2018724225on_trm > set_Pr1481565921on_trm > $o ).
thf(func_def_180,type,
member1978718144riable: produc432717079riable > set_Pr181266295riable > $o ).
thf(func_def_181,type,
member2122665623le_trm: produc1367888000le_trm > set_Pr1235432374le_trm > $o ).
thf(func_def_182,type,
member694524327on_trm: produc464795408on_trm > set_Pr943832262on_trm > $o ).
thf(func_def_183,type,
member1866856748r_char: produc1593312387r_char > set_Pr604539619r_char > $o ).
thf(func_def_184,type,
member1735386832rm_trm: product_prod_trm_trm > set_Pr491793543rm_trm > $o ).
thf(func_def_185,type,
member_char: char > set_char > $o ).
thf(func_def_186,type,
member_variable: variable > set_variable > $o ).
thf(func_def_187,type,
u: set_variable ).
thf(func_def_188,type,
ua: set_variable ).
thf(func_def_189,type,
eta: trm ).
thf(func_def_190,type,
nu: variable > real ).
thf(func_def_191,type,
nu2: variable > real ).
thf(func_def_192,type,
omega: variable > real ).
thf(func_def_193,type,
omega2: variable > real ).
thf(func_def_194,type,
sigma: produc1418842292n_game ).
thf(func_def_195,type,
theta: trm ).
thf(func_def_212,type,
sK0: produc1699626005le_trm > produc1418842292n_game ).
thf(func_def_213,type,
sK1: produc1699626005le_trm > real ).
thf(func_def_214,type,
sK2: produc1699626005le_trm > set_variable ).
thf(func_def_215,type,
sK3: produc1699626005le_trm > char ).
thf(func_def_216,type,
sK4: produc1699626005le_trm > produc1418842292n_game ).
thf(func_def_217,type,
sK5: produc1699626005le_trm > set_variable ).
thf(func_def_218,type,
sK6: produc1699626005le_trm > trm ).
thf(func_def_219,type,
sK7: produc1699626005le_trm > char ).
thf(func_def_220,type,
sK8: produc1699626005le_trm > set_variable ).
thf(func_def_221,type,
sK9: produc1699626005le_trm > produc1418842292n_game ).
thf(func_def_222,type,
sK10: produc1699626005le_trm > trm ).
thf(func_def_223,type,
sK11: produc1699626005le_trm > trm ).
thf(func_def_224,type,
sK12: produc1699626005le_trm > set_variable ).
thf(func_def_225,type,
sK13: produc1699626005le_trm > produc1418842292n_game ).
thf(func_def_226,type,
sK14: produc1699626005le_trm > set_variable ).
thf(func_def_227,type,
sK15: produc1699626005le_trm > trm ).
thf(func_def_228,type,
sK16: produc1699626005le_trm > produc1418842292n_game ).
thf(func_def_229,type,
sK17: produc1699626005le_trm > produc1418842292n_game ).
thf(func_def_230,type,
sK18: produc1699626005le_trm > variable ).
thf(func_def_231,type,
sK19: produc1699626005le_trm > set_variable ).
thf(func_def_232,type,
sK20: produc1699626005le_trm > set_variable ).
thf(func_def_233,type,
sK21: produc1699626005le_trm > produc1418842292n_game ).
thf(func_def_234,type,
sK22: produc1699626005le_trm > trm ).
thf(func_def_235,type,
sK23: produc1699626005le_trm > trm ).
thf(func_def_237,type,
ph25:
!>[X0: $tType] : X0 ).
thf(f959,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f958]) ).
thf(f958,plain,
none_fml != none_fml,
inference(superposition,[status(thm)],[f943,f956]) ).
thf(f956,plain,
! [X0: trm] :
( none_fml
= ( uSubst516392804stappf @ sigma @ ua @ ( geq @ theta @ X0 ) ) ),
inference(equality_resolution,[status(thm)],[f953]) ).
thf(f953,plain,
! [X2: trm,X3: trm,X0: set_variable,X1: produc1418842292n_game] :
( ( ( uSubst516392818stappt @ sigma @ ua @ theta )
!= ( uSubst516392818stappt @ X1 @ X0 @ X3 ) )
| ( none_fml
= ( uSubst516392804stappf @ X1 @ X0 @ ( geq @ X3 @ X2 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f933,f937]) ).
thf(f937,plain,
( none_trm
= ( uSubst516392818stappt @ sigma @ ua @ theta ) ),
inference(cnf_transformation,[status(thm)],[f866]) ).
thf(f866,plain,
( none_trm
= ( uSubst516392818stappt @ sigma @ ua @ theta ) ),
inference(flattening,[status(thm)],[f354]) ).
thf(f354,negated_conjecture,
~ ( ( none_trm
!= ( uSubst516392818stappt @ sigma @ ua @ theta ) ) ),
inference(negated_conjecture,[status(cth)],[f353]) ).
thf(f353,conjecture,
( none_trm
!= ( uSubst516392818stappt @ sigma @ ua @ theta ) ),
file('/export/starexec/sandbox/tmp/tmp.Mj9VJvCut7/DTF2THF_26624.p',conj_0) ).
thf(f933,plain,
! [X2: trm,X3: trm,X0: set_variable,X1: produc1418842292n_game] :
( ( none_fml
= ( uSubst516392804stappf @ X1 @ X0 @ ( geq @ X3 @ X2 ) ) )
| ( none_trm
!= ( uSubst516392818stappt @ X1 @ X0 @ X3 ) ) ),
inference(cnf_transformation,[status(thm)],[f896]) ).
thf(f896,plain,
! [X0: set_variable,X1: produc1418842292n_game,X2: trm,X3: trm] :
( ( none_fml
= ( uSubst516392804stappf @ X1 @ X0 @ ( geq @ X3 @ X2 ) ) )
| ( ( none_trm
!= ( uSubst516392818stappt @ X1 @ X0 @ X2 ) )
& ( none_trm
!= ( uSubst516392818stappt @ X1 @ X0 @ X3 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f876]) ).
thf(f876,plain,
! [X0: set_variable,X1: produc1418842292n_game,X2: trm,X3: trm] :
( ( none_fml
!= ( uSubst516392804stappf @ X1 @ X0 @ ( geq @ X3 @ X2 ) ) )
=> ( ( none_trm
!= ( uSubst516392818stappt @ X1 @ X0 @ X2 ) )
& ( none_trm
!= ( uSubst516392818stappt @ X1 @ X0 @ X3 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X1: set_variable,X0: produc1418842292n_game,X3: trm,X2: trm] :
( ( ( uSubst516392804stappf @ X0 @ X1 @ ( geq @ X2 @ X3 ) )
!= none_fml )
=> ( ( none_trm
!= ( uSubst516392818stappt @ X0 @ X1 @ X3 ) )
& ( ( uSubst516392818stappt @ X0 @ X1 @ X2 )
!= none_trm ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Mj9VJvCut7/DTF2THF_26624.p',fact_1_usubstappf__geq__conv) ).
thf(f943,plain,
( none_fml
!= ( uSubst516392804stappf @ sigma @ ua @ ( geq @ theta @ eta ) ) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
thf(f3,axiom,
( none_fml
!= ( uSubst516392804stappf @ sigma @ ua @ ( geq @ theta @ eta ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Mj9VJvCut7/DTF2THF_26624.p',fact_2_Geq_Oprems_I1_J) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : ITP200^1 : TPTP v9.2.1. Released v7.5.0.
% 0.11/0.14 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.14/0.37 % Computer : n003.cluster.edu
% 0.14/0.37 % Model : x86_64 x86_64
% 0.14/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37 % Memory : 8042.1875MB
% 0.14/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37 % CPULimit : 300
% 0.14/0.37 % WCLimit : 300
% 0.14/0.37 % DateTime : Tue Feb 24 08:36:41 EST 2026
% 0.14/0.37 % CPUTime :
% 0.14/0.37 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.25/0.48 ---- Original DTF file ---
% 0.25/0.49 thf(spec,logic,$$dhol).
% 0.25/0.49 %------------------------------------------------------------------------------
% 0.25/0.49 % File : ITP200^1 : TPTP v9.2.1. Released v7.5.0.
% 0.25/0.49 % Domain : Interactive Theorem Proving
% 0.25/0.49 % Problem : Sledgehammer USubst problem prob_1407__6352118_1
% 0.25/0.49 % Version : Especial.
% 0.25/0.49 % English :
% 0.25/0.49
% 0.25/0.49 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.25/0.49 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.25/0.49 % Source : [Des21]
% 0.25/0.49 % Names : USubst/prob_1407__6352118_1 [Des21]
% 0.25/0.49
% 0.25/0.49 % Status : Theorem
% 0.25/0.49 % Rating : 0.22 v9.1.0, 0.12 v9.0.0, 0.30 v8.2.0, 0.23 v8.1.0, 0.27 v7.5.0
% 0.25/0.49 % Syntax : Number of formulae : 549 ( 161 unt; 196 typ; 0 def)
% 0.25/0.49 % Number of atoms : 1044 ( 570 equ; 0 cnn)
% 0.25/0.49 % Maximal formula atoms : 17 ( 2 avg)
% 0.25/0.49 % Number of connectives : 3358 ( 206 ~; 13 |; 55 &;2450 @)
% 0.25/0.49 % ( 0 <=>; 634 =>; 0 <=; 0 <~>)
% 0.25/0.49 % Maximal formula depth : 19 ( 7 avg)
% 0.25/0.49 % Number of types : 52 ( 51 usr)
% 0.25/0.49 % Number of type conns : 638 ( 638 >; 0 *; 0 +; 0 <<)
% 0.25/0.49 % Number of symbols : 148 ( 145 usr; 10 con; 0-3 aty)
% 0.25/0.49 % Number of variables : 1316 ( 173 ^;1110 !; 33 ?;1316 :)
% 0.25/0.49 % SPC : TH0_THM_EQU_NAR
% 0.25/0.49
% 0.25/0.49 % Comments : This file was generated by Sledgehammer 2021-02-23 15:38:23.912
% 0.25/0.49 %------------------------------------------------------------------------------
% 0.25/0.49 % Could-be-implicit typings (51)
% 0.25/0.49 thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_I_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ofml_J_J_M_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ogame_J_J_J_J_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Syntax__Otrm_J_J,type,
% 0.25/0.49 produc1699626005le_trm: $tType ).
% 0.25/0.49
% 0.25/0.49 thf(ty_n_t__Product____Type__Oprod_I_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ofml_J_J_M_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ogame_J_J_J_J_J,type,
% 0.25/0.49 produc1418842292n_game: $tType ).
% 0.25/0.49
% 0.25/0.49 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ogame_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J_Mt__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ogame_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J_J_J,type,
% 0.25/0.49 set_Pr1918373977on_fml: $tType ).
% 0.25/0.49
% 0.25/0.49 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Otrm_J_Mt__Option__Ooption_It__Syntax__Otrm_J_J_Mt__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Otrm_J_Mt__Option__Ooption_It__Syntax__Otrm_J_J_J_J,type,
% 0.25/0.49 set_Pr1062384839on_trm: $tType ).
% 0.25/0.49
% 0.25/0.49 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Otrm_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J_Mt__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Otrm_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J_J_J,type,
% 0.25/0.49 set_Pr519625031on_fml: $tType ).
% 0.25/0.49
% 0.25/0.49 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ofml_J_Mt__Option__Ooption_It__Syntax__Otrm_J_J_Mt__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ofml_J_Mt__Option__Ooption_It__Syntax__Otrm_J_J_J_J,type,
% 0.25/0.49 set_Pr1588097095on_trm: $tType ).
% 0.25/0.49
% 0.25/0.49 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ofml_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J_Mt__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ofml_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J_J_J,type,
% 0.25/0.49 set_Pr1045337287on_fml: $tType ).
% 0.25/0.49
% 0.25/0.49 thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ogame_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J_Mt__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ogame_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J_J,type,
% 0.25/0.49 produc1928189433on_fml: $tType ).
% 0.25/0.49
% 0.25/0.49 thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Otrm_J_Mt__Option__Ooption_It__Syntax__Otrm_J_J_Mt__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Otrm_J_Mt__Option__Ooption_It__Syntax__Otrm_J_J_J,type,
% 0.25/0.49 produc2024965863on_trm: $tType ).
% 0.25/0.49
% 0.25/0.49 thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Otrm_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J_Mt__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Otrm_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J_J,type,
% 0.25/0.49 produc591588199on_fml: $tType ).
% 0.25/0.49
% 0.25/0.49 thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ofml_J_Mt__Option__Ooption_It__Syntax__Otrm_J_J_Mt__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ofml_J_Mt__Option__Ooption_It__Syntax__Otrm_J_J_J,type,
% 0.25/0.49 produc1158546023on_trm: $tType ).
% 0.25/0.49
% 0.25/0.49 thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ofml_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J_Mt__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ofml_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J_J,type,
% 0.25/0.49 produc1872652007on_fml: $tType ).
% 0.25/0.49
% 0.25/0.49 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_Mt__Product____Type__Oprod_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_J_J,type,
% 0.25/0.49 set_Pr1481565921on_trm: $tType ).
% 0.25/0.49
% 0.25/0.49 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Syntax__Otrm_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Syntax__Otrm_J_J_J,type,
% 0.25/0.49 set_Pr1969262145le_trm: $tType ).
% 0.25/0.49
% 0.25/0.49 thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_Mt__Product____Type__Oprod_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_J,type,
% 0.25/0.49 produc2018724225on_trm: $tType ).
% 0.25/0.49
% 0.25/0.49 thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Syntax__Otrm_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Syntax__Otrm_J_J,type,
% 0.25/0.49 produc1279577057le_trm: $tType ).
% 0.25/0.49
% 0.25/0.49 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ogame_J_Mt__Option__Ooption_It__Syntax__Ogame_J_J_J,type,
% 0.25/0.49 set_Pr1625152599n_game: $tType ).
% 0.25/0.49
% 0.25/0.49 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ogame_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J_J,type,
% 0.25/0.49 set_Pr622314946on_fml: $tType ).
% 0.25/0.49
% 0.25/0.49 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Otrm_J_Mt__Option__Ooption_It__Syntax__Otrm_J_J_J,type,
% 0.25/0.49 set_Pr1471344007on_trm: $tType ).
% 0.25/0.49
% 0.25/0.49 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ofml_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J_J,type,
% 0.25/0.49 set_Pr927595527on_fml: $tType ).
% 0.25/0.49
% 0.25/0.49 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Set__Oset_It__Syntax__Ovariable_J_J_J,type,
% 0.25/0.49 set_Pr181266295riable: $tType ).
% 0.25/0.49
% 0.25/0.49 thf(ty_n_t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ogame_J_Mt__Option__Ooption_It__Syntax__Ogame_J_J,type,
% 0.25/0.49 produc1016592119n_game: $tType ).
% 0.25/0.49
% 0.25/0.49 thf(ty_n_t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ogame_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J,type,
% 0.25/0.49 produc1739631244on_fml: $tType ).
% 0.25/0.49
% 0.25/0.49 thf(ty_n_t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Otrm_J_Mt__Option__Ooption_It__Syntax__Otrm_J_J,type,
% 0.25/0.49 produc1072747943on_trm: $tType ).
% 0.25/0.49
% 0.25/0.49 thf(ty_n_t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Otrm_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J,type,
% 0.25/0.49 produc1456309597on_fml: $tType ).
% 0.25/0.49
% 0.25/0.49 thf(ty_n_t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ofml_J_Mt__Option__Ooption_It__Syntax__Otrm_J_J,type,
% 0.25/0.49 produc1810527345on_trm: $tType ).
% 0.25/0.49
% 0.25/0.49 thf(ty_n_t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ofml_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J,type,
% 0.25/0.49 produc46605351on_fml: $tType ).
% 0.25/0.49
% 0.25/0.49 thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Set__Oset_It__Syntax__Ovariable_J_J,type,
% 0.25/0.49 produc432717079riable: $tType ).
% 0.25/0.49
% 0.25/0.49 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_J,type,
% 0.25/0.49 set_Pr943832262on_trm: $tType ).
% 0.25/0.49
% 0.25/0.49 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Syntax__Otrm_J_J,type,
% 0.25/0.49 set_Pr1235432374le_trm: $tType ).
% 0.25/0.49
% 0.25/0.49 thf(ty_n_t__Product____Type__Oprod_It__Syntax__Ovariable_Mt__Option__Ooption_It__Syntax__Otrm_J_J,type,
% 0.25/0.49 produc1024976764on_trm: $tType ).
% 0.25/0.49
% 0.25/0.49 thf(ty_n_t__Product____Type__Oprod_It__Syntax__Ovariable_Mt__Option__Ooption_It__Syntax__Ofml_J_J,type,
% 0.25/0.49 produc1408538418on_fml: $tType ).
% 0.25/0.49
% 0.25/0.49 thf(ty_n_t__Product____Type__Oprod_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J,type,
% 0.25/0.49 produc464795408on_trm: $tType ).
% 0.25/0.49
% 0.25/0.49 thf(ty_n_t__Product____Type__Oprod_It__Denotational____Semantics__Ointerp_Mt__Syntax__Otrm_J,type,
% 0.25/0.49 produc833882726rp_trm: $tType ).
% 0.25/0.49
% 0.25/0.49 thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Syntax__Otrm_J,type,
% 0.25/0.49 produc1367888000le_trm: $tType ).
% 0.25/0.49
% 0.25/0.49 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__String__Ochar_Mt__String__Ochar_J_J,type,
% 0.25/0.49 set_Pr604539619r_char: $tType ).
% 0.25/0.49
% 0.25/0.49 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Syntax__Otrm_Mt__Syntax__Otrm_J_J,type,
% 0.25/0.49 set_Pr491793543rm_trm: $tType ).
% 0.25/0.49
% 0.25/0.49 thf(ty_n_t__Product____Type__Oprod_It__String__Ochar_Mt__String__Ochar_J,type,
% 0.25/0.49 produc1593312387r_char: $tType ).
% 0.25/0.49
% 0.25/0.49 thf(ty_n_t__Product____Type__Oprod_It__Syntax__Otrm_Mt__Syntax__Otrm_J,type,
% 0.25/0.49 product_prod_trm_trm: $tType ).
% 0.25/0.49
% 0.25/0.49 thf(ty_n_t__Option__Ooption_It__Syntax__Ogame_J,type,
% 0.25/0.49 option_game: $tType ).
% 0.25/0.49
% 0.25/0.49 thf(ty_n_t__Option__Ooption_It__Syntax__Otrm_J,type,
% 0.25/0.49 option_trm: $tType ).
% 0.25/0.49
% 0.25/0.49 thf(ty_n_t__Option__Ooption_It__Syntax__Ofml_J,type,
% 0.25/0.49 option_fml: $tType ).
% 0.25/0.49
% 0.25/0.49 thf(ty_n_t__Denotational____Semantics__Ointerp,type,
% 0.25/0.49 denotational_interp: $tType ).
% 0.25/0.49
% 0.25/0.49 thf(ty_n_t__Set__Oset_It__Syntax__Ovariable_J,type,
% 0.25/0.49 set_variable: $tType ).
% 0.25/0.49
% 0.25/0.49 thf(ty_n_t__Set__Oset_It__String__Ochar_J,type,
% 0.25/0.49 set_char: $tType ).
% 0.25/0.49
% 0.25/0.49 thf(ty_n_t__Syntax__Ovariable,type,
% 0.25/0.49 variable: $tType ).
% 0.25/0.49
% 0.25/0.49 thf(ty_n_t__Syntax__Ogame,type,
% 0.25/0.49 game: $tType ).
% 0.25/0.49
% 0.25/0.49 thf(ty_n_t__String__Ochar,type,
% 0.25/0.49 char: $tType ).
% 0.25/0.49
% 0.25/0.49 thf(ty_n_t__Syntax__Otrm,type,
% 0.25/0.49 trm: $tType ).
% 0.25/0.49
% 0.25/0.49 thf(ty_n_t__Syntax__Ofml,type,
% 0.25/0.49 fml: $tType ).
% 0.25/0.49
% 0.25/0.49 thf(ty_n_t__Real__Oreal,type,
% 0.25/0.49 real: $tType ).
% 0.25/0.49
% 0.25/0.49 % Explicit typings (145)
% 0.25/0.49 thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001t__String__Ochar_001t__Option__Ooption_It__Syntax__Ofml_J_001t__Option__Ooption_It__Syntax__Ofml_J,type,
% 0.25/0.49 bNF_Gr1866170027on_fml: set_char > ( char > option_fml ) > ( char > option_fml ) > set_Pr927595527on_fml ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001t__String__Ochar_001t__Option__Ooption_It__Syntax__Ogame_J_001t__Option__Ooption_It__Syntax__Ofml_J,type,
% 0.25/0.49 bNF_Gr756940202on_fml: set_char > ( char > option_game ) > ( char > option_fml ) > set_Pr622314946on_fml ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001t__String__Ochar_001t__Option__Ooption_It__Syntax__Otrm_J_001t__Option__Ooption_It__Syntax__Otrm_J,type,
% 0.25/0.49 bNF_Gr1666135339on_trm: set_char > ( char > option_trm ) > ( char > option_trm ) > set_Pr1471344007on_trm ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001t__String__Ochar_001t__Set__Oset_It__Syntax__Ovariable_J_001t__Syntax__Otrm,type,
% 0.25/0.49 bNF_Gr852774302le_trm: set_char > ( char > set_variable ) > ( char > trm ) > set_Pr1235432374le_trm ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001t__String__Ochar_001t__String__Ochar_001t__Option__Ooption_It__Syntax__Otrm_J,type,
% 0.25/0.49 bNF_Gr951178926on_trm: set_char > ( char > char ) > ( char > option_trm ) > set_Pr943832262on_trm ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001t__Syntax__Ovariable_001t__Option__Ooption_It__Syntax__Ofml_J_001t__Option__Ooption_It__Syntax__Ofml_J,type,
% 0.25/0.49 bNF_Gr600956991on_fml: set_variable > ( variable > option_fml ) > ( variable > option_fml ) > set_Pr927595527on_fml ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001t__Syntax__Ovariable_001t__Option__Ooption_It__Syntax__Ogame_J_001t__Option__Ooption_It__Syntax__Ofml_J,type,
% 0.25/0.49 bNF_Gr2142503190on_fml: set_variable > ( variable > option_game ) > ( variable > option_fml ) > set_Pr622314946on_fml ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001t__Syntax__Ovariable_001t__Option__Ooption_It__Syntax__Otrm_J_001t__Option__Ooption_It__Syntax__Otrm_J,type,
% 0.25/0.49 bNF_Gr400922303on_trm: set_variable > ( variable > option_trm ) > ( variable > option_trm ) > set_Pr1471344007on_trm ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001t__Syntax__Ovariable_001t__Set__Oset_It__Syntax__Ovariable_J_001t__Syntax__Otrm,type,
% 0.25/0.49 bNF_Gr1330108682le_trm: set_variable > ( variable > set_variable ) > ( variable > trm ) > set_Pr1235432374le_trm ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001t__Syntax__Ovariable_001t__String__Ochar_001t__Option__Ooption_It__Syntax__Otrm_J,type,
% 0.25/0.49 bNF_Gr1933470746on_trm: set_variable > ( variable > char ) > ( variable > option_trm ) > set_Pr943832262on_trm ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_BNF__Greatest__Fixpoint_OrelImage_001t__Option__Ooption_It__Syntax__Ofml_J_001t__Option__Ooption_It__Syntax__Ofml_J,type,
% 0.25/0.49 bNF_Gr806120164on_fml: set_Pr927595527on_fml > ( option_fml > option_fml ) > set_Pr927595527on_fml ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Denotational__Semantics_OUvariation,type,
% 0.25/0.49 denota1419872369iation: ( variable > real ) > ( variable > real ) > set_variable > $o ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Option_Ooption_ONone_001t__Syntax__Ofml,type,
% 0.25/0.49 none_fml: option_fml ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Option_Ooption_ONone_001t__Syntax__Ogame,type,
% 0.25/0.49 none_game: option_game ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Option_Ooption_ONone_001t__Syntax__Otrm,type,
% 0.25/0.49 none_trm: option_trm ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Option_Ooption_OSome_001t__Syntax__Ofml,type,
% 0.25/0.49 some_fml: fml > option_fml ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Option_Ooption_OSome_001t__Syntax__Ogame,type,
% 0.25/0.49 some_game: game > option_game ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Option_Ooption_OSome_001t__Syntax__Otrm,type,
% 0.25/0.49 some_trm: trm > option_trm ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Option_Ooption_Ocase__option_001_Eo_001t__Syntax__Ofml,type,
% 0.25/0.49 case_option_o_fml: $o > ( fml > $o ) > option_fml > $o ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Option_Ooption_Ocase__option_001_Eo_001t__Syntax__Ogame,type,
% 0.25/0.49 case_option_o_game: $o > ( game > $o ) > option_game > $o ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Option_Ooption_Ocase__option_001_Eo_001t__Syntax__Otrm,type,
% 0.25/0.49 case_option_o_trm: $o > ( trm > $o ) > option_trm > $o ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Option_Ooption_Othe_001t__Syntax__Ofml,type,
% 0.25/0.49 the_fml: option_fml > fml ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Option_Ooption_Othe_001t__Syntax__Ogame,type,
% 0.25/0.49 the_game: option_game > game ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Option_Ooption_Othe_001t__Syntax__Otrm,type,
% 0.25/0.49 the_trm: option_trm > trm ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Option__Ooption_It__Syntax__Ofml_J_M_062_It__Option__Ooption_It__Syntax__Ofml_J_M_Eo_J_J,type,
% 0.25/0.49 ord_le802833166_fml_o: ( option_fml > option_fml > $o ) > ( option_fml > option_fml > $o ) > $o ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Option__Ooption_It__Syntax__Ofml_J_M_Eo_J,type,
% 0.25/0.49 ord_le181580155_fml_o: ( option_fml > $o ) > ( option_fml > $o ) > $o ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Option__Ooption_It__Syntax__Ogame_J_M_062_It__Option__Ooption_It__Syntax__Ofml_J_M_Eo_J_J,type,
% 0.25/0.49 ord_le1588489637_fml_o: ( option_game > option_fml > $o ) > ( option_game > option_fml > $o ) > $o ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Option__Ooption_It__Syntax__Otrm_J_M_062_It__Option__Ooption_It__Syntax__Otrm_J_M_Eo_J_J,type,
% 0.25/0.49 ord_le847028878_trm_o: ( option_trm > option_trm > $o ) > ( option_trm > option_trm > $o ) > $o ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Option__Ooption_It__Syntax__Otrm_J_M_Eo_J,type,
% 0.25/0.49 ord_le1957133745_trm_o: ( option_trm > $o ) > ( option_trm > $o ) > $o ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Otrm_J_Mt__Option__Ooption_It__Syntax__Otrm_J_J_M_062_It__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Otrm_J_Mt__Option__Ooption_It__Syntax__Otrm_J_J_M_Eo_J_J,type,
% 0.25/0.49 ord_le90123726_trm_o: ( produc1072747943on_trm > produc1072747943on_trm > $o ) > ( produc1072747943on_trm > produc1072747943on_trm > $o ) > $o ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Otrm_J_Mt__Option__Ooption_It__Syntax__Otrm_J_J_M_Eo_J,type,
% 0.25/0.49 ord_le1721128566_trm_o: ( produc1072747943on_trm > $o ) > ( produc1072747943on_trm > $o ) > $o ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Product____Type__Oprod_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_M_062_It__Product____Type__Oprod_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_M_Eo_J_J,type,
% 0.25/0.49 ord_le157637894_trm_o: ( produc464795408on_trm > produc464795408on_trm > $o ) > ( produc464795408on_trm > produc464795408on_trm > $o ) > $o ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Product____Type__Oprod_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_M_Eo_J,type,
% 0.25/0.49 ord_le1222882015_trm_o: ( produc464795408on_trm > $o ) > ( produc464795408on_trm > $o ) > $o ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Product____Type__Oprod_It__Syntax__Ovariable_Mt__Option__Ooption_It__Syntax__Otrm_J_J_M_062_It__Product____Type__Oprod_It__Syntax__Ovariable_Mt__Option__Ooption_It__Syntax__Otrm_J_J_M_Eo_J_J,type,
% 0.25/0.49 ord_le370603054_trm_o: ( produc1024976764on_trm > produc1024976764on_trm > $o ) > ( produc1024976764on_trm > produc1024976764on_trm > $o ) > $o ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Product____Type__Oprod_It__Syntax__Ovariable_Mt__Option__Ooption_It__Syntax__Otrm_J_J_M_Eo_J,type,
% 0.25/0.49 ord_le373274227_trm_o: ( produc1024976764on_trm > $o ) > ( produc1024976764on_trm > $o ) > $o ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Set__Oset_It__Syntax__Ovariable_J_M_062_It__Syntax__Otrm_M_Eo_J_J,type,
% 0.25/0.49 ord_le691957041_trm_o: ( set_variable > trm > $o ) > ( set_variable > trm > $o ) > $o ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__String__Ochar_M_062_It__Option__Ooption_It__Syntax__Otrm_J_M_Eo_J_J,type,
% 0.25/0.49 ord_le1890124833_trm_o: ( char > option_trm > $o ) > ( char > option_trm > $o ) > $o ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__String__Ochar_M_Eo_J,type,
% 0.25/0.49 ord_less_eq_char_o: ( char > $o ) > ( char > $o ) > $o ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Syntax__Ovariable_M_Eo_J,type,
% 0.25/0.49 ord_le1407353162able_o: ( variable > $o ) > ( variable > $o ) > $o ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ofml_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J_J,type,
% 0.25/0.49 ord_le778974119on_fml: set_Pr927595527on_fml > set_Pr927595527on_fml > $o ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ogame_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J_J,type,
% 0.25/0.49 ord_le782333474on_fml: set_Pr622314946on_fml > set_Pr622314946on_fml > $o ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Otrm_J_Mt__Option__Ooption_It__Syntax__Otrm_J_J_J,type,
% 0.25/0.49 ord_le1322722599on_trm: set_Pr1471344007on_trm > set_Pr1471344007on_trm > $o ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Syntax__Otrm_J_J,type,
% 0.25/0.49 ord_le2102862870le_trm: set_Pr1235432374le_trm > set_Pr1235432374le_trm > $o ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_J,type,
% 0.25/0.49 ord_le541293862on_trm: set_Pr943832262on_trm > set_Pr943832262on_trm > $o ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__String__Ochar_J,type,
% 0.25/0.49 ord_less_eq_set_char: set_char > set_char > $o ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Syntax__Ovariable_J,type,
% 0.25/0.49 ord_le282106107riable: set_variable > set_variable > $o ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Orderings_Oorder__class_OGreatest_001t__Set__Oset_It__Syntax__Ovariable_J,type,
% 0.25/0.49 order_272405634riable: ( set_variable > $o ) > set_variable ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Product__Type_OPair_001t__Denotational____Semantics__Ointerp_001t__Syntax__Otrm,type,
% 0.25/0.49 produc1132922070rp_trm: denotational_interp > trm > produc833882726rp_trm ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Product__Type_OPair_001t__Option__Ooption_It__Syntax__Ofml_J_001t__Option__Ooption_It__Syntax__Ofml_J,type,
% 0.25/0.49 produc909629463on_fml: option_fml > option_fml > produc46605351on_fml ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Product__Type_OPair_001t__Option__Ooption_It__Syntax__Ofml_J_001t__Option__Ooption_It__Syntax__Otrm_J,type,
% 0.25/0.49 produc1447374177on_trm: option_fml > option_trm > produc1810527345on_trm ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Product__Type_OPair_001t__Option__Ooption_It__Syntax__Ogame_J_001t__Option__Ooption_It__Syntax__Ofml_J,type,
% 0.25/0.49 produc2124676926on_fml: option_game > option_fml > produc1739631244on_fml ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Product__Type_OPair_001t__Option__Ooption_It__Syntax__Ogame_J_001t__Option__Ooption_It__Syntax__Ogame_J,type,
% 0.25/0.49 produc1111617711n_game: option_game > option_game > produc1016592119n_game ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Product__Type_OPair_001t__Option__Ooption_It__Syntax__Otrm_J_001t__Option__Ooption_It__Syntax__Ofml_J,type,
% 0.25/0.49 produc171850061on_fml: option_trm > option_fml > produc1456309597on_fml ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Product__Type_OPair_001t__Option__Ooption_It__Syntax__Otrm_J_001t__Option__Ooption_It__Syntax__Otrm_J,type,
% 0.25/0.49 produc709594775on_trm: option_trm > option_trm > produc1072747943on_trm ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_I_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ofml_J_J_M_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ogame_J_J_J_J_J_001t__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Syntax__Otrm_J,type,
% 0.25/0.49 produc2015636557le_trm: produc1418842292n_game > produc1367888000le_trm > produc1699626005le_trm ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ofml_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J_001t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ofml_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J,type,
% 0.25/0.49 produc1367044951on_fml: produc46605351on_fml > produc46605351on_fml > produc1872652007on_fml ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ofml_J_Mt__Option__Ooption_It__Syntax__Otrm_J_J_001t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ofml_J_Mt__Option__Ooption_It__Syntax__Otrm_J_J,type,
% 0.25/0.49 produc2132972503on_trm: produc1810527345on_trm > produc1810527345on_trm > produc1158546023on_trm ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ogame_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J_001t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ogame_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J,type,
% 0.25/0.49 produc556056113on_fml: produc1739631244on_fml > produc1739631244on_fml > produc1928189433on_fml ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Otrm_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J_001t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Otrm_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J,type,
% 0.25/0.49 produc1235825367on_fml: produc1456309597on_fml > produc1456309597on_fml > produc591588199on_fml ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Otrm_J_Mt__Option__Ooption_It__Syntax__Otrm_J_J_001t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Otrm_J_Mt__Option__Ooption_It__Syntax__Otrm_J_J,type,
% 0.25/0.49 produc2001752919on_trm: produc1072747943on_trm > produc1072747943on_trm > produc2024965863on_trm ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Syntax__Otrm_J_001t__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Syntax__Otrm_J,type,
% 0.25/0.49 produc1056455193le_trm: produc1367888000le_trm > produc1367888000le_trm > produc1279577057le_trm ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_001t__Product____Type__Oprod_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J,type,
% 0.25/0.49 produc444919481on_trm: produc464795408on_trm > produc464795408on_trm > produc2018724225on_trm ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Syntax__Ovariable_J_001t__Set__Oset_It__Syntax__Ovariable_J,type,
% 0.25/0.49 produc1766592463riable: set_variable > set_variable > produc432717079riable ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Syntax__Ovariable_J_001t__Syntax__Otrm,type,
% 0.25/0.49 produc1482344242le_trm: set_variable > trm > produc1367888000le_trm ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Product__Type_OPair_001t__String__Ochar_001t__Option__Ooption_It__Syntax__Otrm_J,type,
% 0.25/0.49 produc1500300866on_trm: char > option_trm > produc464795408on_trm ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Product__Type_OPair_001t__String__Ochar_001t__String__Ochar,type,
% 0.25/0.49 produc19545147r_char: char > char > produc1593312387r_char ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Product__Type_OPair_001t__Syntax__Otrm_001t__Syntax__Otrm,type,
% 0.25/0.49 product_Pair_trm_trm: trm > trm > product_prod_trm_trm ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Product__Type_OPair_001t__Syntax__Ovariable_001t__Option__Ooption_It__Syntax__Ofml_J,type,
% 0.25/0.49 produc1205977188on_fml: variable > option_fml > produc1408538418on_fml ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Product__Type_OPair_001t__Syntax__Ovariable_001t__Option__Ooption_It__Syntax__Otrm_J,type,
% 0.25/0.49 produc1743721902on_trm: variable > option_trm > produc1024976764on_trm ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ofml_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J,type,
% 0.25/0.49 collec670974098on_fml: ( produc46605351on_fml > $o ) > set_Pr927595527on_fml ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ogame_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J,type,
% 0.25/0.49 collec749447393on_fml: ( produc1739631244on_fml > $o ) > set_Pr622314946on_fml ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Otrm_J_Mt__Option__Ooption_It__Syntax__Otrm_J_J,type,
% 0.25/0.49 collec1697116690on_trm: ( produc1072747943on_trm > $o ) > set_Pr1471344007on_trm ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Syntax__Otrm_J,type,
% 0.25/0.49 collec575343829le_trm: ( produc1367888000le_trm > $o ) > set_Pr1235432374le_trm ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J,type,
% 0.25/0.49 collec1756633317on_trm: ( produc464795408on_trm > $o ) > set_Pr943832262on_trm ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Set_OCollect_001t__String__Ochar,type,
% 0.25/0.49 collect_char: ( char > $o ) > set_char ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Set_OCollect_001t__Syntax__Ovariable,type,
% 0.25/0.49 collect_variable: ( variable > $o ) > set_variable ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Syntax_Ofml_OGeq,type,
% 0.25/0.49 geq: trm > trm > fml ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Syntax_Ogame_OAssign,type,
% 0.25/0.49 assign: variable > trm > game ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Syntax_Ogame_OODE,type,
% 0.25/0.49 ode: char > trm > game ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Syntax_Ogame_OTest,type,
% 0.25/0.49 test: fml > game ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Syntax_Otrm_OConst,type,
% 0.25/0.49 const: char > trm ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Syntax_Otrm_ODifferential,type,
% 0.25/0.49 differential: trm > trm ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Syntax_Otrm_OFunc,type,
% 0.25/0.49 func: char > trm > trm ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Syntax_Otrm_ONumber,type,
% 0.25/0.49 number: real > trm ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Syntax_Otrm_OPlus,type,
% 0.25/0.49 plus: trm > trm > trm ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Syntax_Otrm_OTimes,type,
% 0.25/0.49 times: trm > trm > trm ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Syntax_Otrm_OVar,type,
% 0.25/0.49 var: variable > trm ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_OAssigno,type,
% 0.25/0.49 uSubst834381837ssigno: variable > option_trm > option_game ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_OAssigno__rel,type,
% 0.25/0.49 uSubst157155628no_rel: produc1024976764on_trm > produc1024976764on_trm > $o ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_ODifferentialo,type,
% 0.25/0.49 uSubst716837505ntialo: option_trm > option_trm ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_ODifferentialo__rel,type,
% 0.25/0.49 uSubst2051024824lo_rel: option_trm > option_trm > $o ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_OGeqo,type,
% 0.25/0.49 uSubst152838031e_Geqo: option_trm > option_trm > option_fml ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_OGeqo__rel,type,
% 0.25/0.49 uSubst1304144938qo_rel: produc1072747943on_trm > produc1072747943on_trm > $o ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_OODEo,type,
% 0.25/0.49 uSubst1827052306e_ODEo: char > option_trm > option_game ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_OODEo__rel,type,
% 0.25/0.49 uSubst299938919Eo_rel: produc464795408on_trm > produc464795408on_trm > $o ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_OPluso,type,
% 0.25/0.49 uSubst141955042_Pluso: option_trm > option_trm > option_trm ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_OPluso__rel,type,
% 0.25/0.49 uSubst691094423so_rel: produc1072747943on_trm > produc1072747943on_trm > $o ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_OTesto,type,
% 0.25/0.49 uSubst1367128042_Testo: option_fml > option_game ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_OTesto__rel,type,
% 0.25/0.49 uSubst954181007to_rel: option_fml > option_fml > $o ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_OTimeso,type,
% 0.25/0.49 uSubst918876924Timeso: option_trm > option_trm > option_trm ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_OTimeso__rel,type,
% 0.25/0.49 uSubst924844285so_rel: produc1072747943on_trm > produc1072747943on_trm > $o ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_Ousappconst,type,
% 0.25/0.49 uSubst1559070963pconst: produc1418842292n_game > set_variable > char > option_trm ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_Ousubstappf,type,
% 0.25/0.49 uSubst516392804stappf: produc1418842292n_game > set_variable > fml > option_fml ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_Ousubstappt,type,
% 0.25/0.49 uSubst516392818stappt: produc1418842292n_game > set_variable > trm > option_trm ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_Ousubstappt__rel,type,
% 0.25/0.49 uSubst1917534215pt_rel: produc1699626005le_trm > produc1699626005le_trm > $o ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Wellfounded_Oaccp_001t__Option__Ooption_It__Syntax__Ofml_J,type,
% 0.25/0.49 accp_option_fml: ( option_fml > option_fml > $o ) > option_fml > $o ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Wellfounded_Oaccp_001t__Option__Ooption_It__Syntax__Otrm_J,type,
% 0.25/0.49 accp_option_trm: ( option_trm > option_trm > $o ) > option_trm > $o ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Otrm_J_Mt__Option__Ooption_It__Syntax__Otrm_J_J,type,
% 0.25/0.49 accp_P758790320on_trm: ( produc1072747943on_trm > produc1072747943on_trm > $o ) > produc1072747943on_trm > $o ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Product____Type__Oprod_I_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ofml_J_J_M_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ogame_J_J_J_J_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Syntax__Otrm_J_J,type,
% 0.25/0.49 accp_P1877119646le_trm: ( produc1699626005le_trm > produc1699626005le_trm > $o ) > produc1699626005le_trm > $o ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J,type,
% 0.25/0.49 accp_P419951815on_trm: ( produc464795408on_trm > produc464795408on_trm > $o ) > produc464795408on_trm > $o ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Syntax__Ovariable_Mt__Option__Ooption_It__Syntax__Otrm_J_J,type,
% 0.25/0.49 accp_P394694195on_trm: ( produc1024976764on_trm > produc1024976764on_trm > $o ) > produc1024976764on_trm > $o ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Wellfounded_Olex__prod_001t__Option__Ooption_It__Syntax__Ofml_J_001t__Option__Ooption_It__Syntax__Ofml_J,type,
% 0.25/0.49 lex_pr314879023on_fml: set_Pr927595527on_fml > set_Pr927595527on_fml > set_Pr1045337287on_fml ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Wellfounded_Olex__prod_001t__Option__Ooption_It__Syntax__Ofml_J_001t__Option__Ooption_It__Syntax__Otrm_J,type,
% 0.25/0.49 lex_pr852623737on_trm: set_Pr927595527on_fml > set_Pr1471344007on_trm > set_Pr1588097095on_trm ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Wellfounded_Olex__prod_001t__Option__Ooption_It__Syntax__Ogame_J_001t__Option__Ooption_It__Syntax__Ofml_J,type,
% 0.25/0.49 lex_pr425996582on_fml: set_Pr1625152599n_game > set_Pr927595527on_fml > set_Pr1918373977on_fml ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Wellfounded_Olex__prod_001t__Option__Ooption_It__Syntax__Otrm_J_001t__Option__Ooption_It__Syntax__Ofml_J,type,
% 0.25/0.49 lex_pr1724583269on_fml: set_Pr1471344007on_trm > set_Pr927595527on_fml > set_Pr519625031on_fml ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Wellfounded_Olex__prod_001t__Option__Ooption_It__Syntax__Otrm_J_001t__Option__Ooption_It__Syntax__Otrm_J,type,
% 0.25/0.49 lex_pr114844335on_trm: set_Pr1471344007on_trm > set_Pr1471344007on_trm > set_Pr1062384839on_trm ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Wellfounded_Olex__prod_001t__Set__Oset_It__Syntax__Ovariable_J_001t__Syntax__Otrm,type,
% 0.25/0.49 lex_pr1522821402le_trm: set_Pr181266295riable > set_Pr491793543rm_trm > set_Pr1969262145le_trm ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Wellfounded_Olex__prod_001t__String__Ochar_001t__Option__Ooption_It__Syntax__Otrm_J,type,
% 0.25/0.49 lex_pr1901327402on_trm: set_Pr604539619r_char > set_Pr1471344007on_trm > set_Pr1481565921on_trm ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_member_001t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ofml_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J,type,
% 0.25/0.49 member1287158352on_fml: produc46605351on_fml > set_Pr927595527on_fml > $o ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_member_001t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ogame_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J,type,
% 0.25/0.49 member1883102883on_fml: produc1739631244on_fml > set_Pr622314946on_fml > $o ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_member_001t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ogame_J_Mt__Option__Ooption_It__Syntax__Ogame_J_J,type,
% 0.25/0.49 member191809696n_game: produc1016592119n_game > set_Pr1625152599n_game > $o ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_member_001t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Otrm_J_Mt__Option__Ooption_It__Syntax__Otrm_J_J,type,
% 0.25/0.49 member165817296on_trm: produc1072747943on_trm > set_Pr1471344007on_trm > $o ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ofml_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J_Mt__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ofml_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J_J,type,
% 0.25/0.49 member450497296on_fml: produc1872652007on_fml > set_Pr1045337287on_fml > $o ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ofml_J_Mt__Option__Ooption_It__Syntax__Otrm_J_J_Mt__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ofml_J_Mt__Option__Ooption_It__Syntax__Otrm_J_J_J,type,
% 0.25/0.49 member1883874960on_trm: produc1158546023on_trm > set_Pr1588097095on_trm > $o ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ogame_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J_Mt__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ogame_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J_J,type,
% 0.25/0.49 member113767842on_fml: produc1928189433on_fml > set_Pr1918373977on_fml > $o ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Otrm_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J_Mt__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Otrm_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J_J,type,
% 0.25/0.49 member1316917136on_fml: produc591588199on_fml > set_Pr519625031on_fml > $o ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Otrm_J_Mt__Option__Ooption_It__Syntax__Otrm_J_J_Mt__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Otrm_J_Mt__Option__Ooption_It__Syntax__Otrm_J_J_J,type,
% 0.25/0.49 member602811152on_trm: produc2024965863on_trm > set_Pr1062384839on_trm > $o ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Syntax__Otrm_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Syntax__Otrm_J_J,type,
% 0.25/0.49 member1150310282le_trm: produc1279577057le_trm > set_Pr1969262145le_trm > $o ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_Mt__Product____Type__Oprod_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_J,type,
% 0.25/0.49 member1950256170on_trm: produc2018724225on_trm > set_Pr1481565921on_trm > $o ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Set__Oset_It__Syntax__Ovariable_J_J,type,
% 0.25/0.49 member1978718144riable: produc432717079riable > set_Pr181266295riable > $o ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Syntax__Otrm_J,type,
% 0.25/0.49 member2122665623le_trm: produc1367888000le_trm > set_Pr1235432374le_trm > $o ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_member_001t__Product____Type__Oprod_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J,type,
% 0.25/0.49 member694524327on_trm: produc464795408on_trm > set_Pr943832262on_trm > $o ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_member_001t__Product____Type__Oprod_It__String__Ochar_Mt__String__Ochar_J,type,
% 0.25/0.49 member1866856748r_char: produc1593312387r_char > set_Pr604539619r_char > $o ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_member_001t__Product____Type__Oprod_It__Syntax__Otrm_Mt__Syntax__Otrm_J,type,
% 0.25/0.49 member1735386832rm_trm: product_prod_trm_trm > set_Pr491793543rm_trm > $o ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_member_001t__String__Ochar,type,
% 0.25/0.49 member_char: char > set_char > $o ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_member_001t__Syntax__Ovariable,type,
% 0.25/0.49 member_variable: variable > set_variable > $o ).
% 0.25/0.49
% 0.25/0.49 thf(sy_v_U,type,
% 0.25/0.49 u: set_variable ).
% 0.25/0.49
% 0.25/0.49 thf(sy_v_Ua____,type,
% 0.25/0.49 ua: set_variable ).
% 0.25/0.49
% 0.25/0.49 thf(sy_v__092_060eta_062____,type,
% 0.25/0.49 eta: trm ).
% 0.25/0.49
% 0.25/0.49 thf(sy_v__092_060nu_062,type,
% 0.25/0.49 nu: variable > real ).
% 0.25/0.49
% 0.25/0.49 thf(sy_v__092_060nu_062_H____,type,
% 0.25/0.49 nu2: variable > real ).
% 0.25/0.49
% 0.25/0.49 thf(sy_v__092_060omega_062,type,
% 0.25/0.49 omega: variable > real ).
% 0.25/0.49
% 0.25/0.49 thf(sy_v__092_060omega_062_H____,type,
% 0.25/0.49 omega2: variable > real ).
% 0.25/0.49
% 0.25/0.49 thf(sy_v__092_060sigma_062_H_H____,type,
% 0.25/0.49 sigma: produc1418842292n_game ).
% 0.25/0.49
% 0.25/0.49 thf(sy_v__092_060theta_062____,type,
% 0.25/0.49 theta: trm ).
% 0.25/0.49
% 0.25/0.49 % Relevant facts (352)
% 0.25/0.49 thf(fact_0_vaouter,axiom,
% 0.25/0.49 denota1419872369iation @ nu @ omega @ u ).
% 0.25/0.49
% 0.25/0.49 % vaouter
% 0.25/0.49 thf(fact_1_usubstappf__geq__conv,axiom,
% 0.25/0.49 ! [Sigma: produc1418842292n_game,U: set_variable,Theta: trm,Eta: trm] :
% 0.25/0.49 ( ( ( uSubst516392804stappf @ Sigma @ U @ ( geq @ Theta @ Eta ) )
% 0.25/0.49 != none_fml )
% 0.25/0.49 => ( ( ( uSubst516392818stappt @ Sigma @ U @ Theta )
% 0.25/0.49 != none_trm )
% 0.25/0.49 & ( ( uSubst516392818stappt @ Sigma @ U @ Eta )
% 0.25/0.49 != none_trm ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % usubstappf_geq_conv
% 0.25/0.49 thf(fact_2_Geq_Oprems_I1_J,axiom,
% 0.25/0.49 ( ( uSubst516392804stappf @ sigma @ ua @ ( geq @ theta @ eta ) )
% 0.25/0.49 != none_fml ) ).
% 0.25/0.49
% 0.25/0.49 % Geq.prems(1)
% 0.25/0.49 thf(fact_3_undeft__None,axiom,
% 0.25/0.49 none_trm = none_trm ).
% 0.25/0.49
% 0.25/0.49 % undeft_None
% 0.25/0.49 thf(fact_4_usubstappt__det,axiom,
% 0.25/0.49 ! [Sigma: produc1418842292n_game,U: set_variable,Theta: trm,V: set_variable] :
% 0.25/0.49 ( ( ( uSubst516392818stappt @ Sigma @ U @ Theta )
% 0.25/0.49 != none_trm )
% 0.25/0.49 => ( ( ( uSubst516392818stappt @ Sigma @ V @ Theta )
% 0.25/0.49 != none_trm )
% 0.25/0.49 => ( ( uSubst516392818stappt @ Sigma @ U @ Theta )
% 0.25/0.49 = ( uSubst516392818stappt @ Sigma @ V @ Theta ) ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % usubstappt_det
% 0.25/0.49 thf(fact_5_Geq_Oprems_I2_J,axiom,
% 0.25/0.49 denota1419872369iation @ nu2 @ omega2 @ ua ).
% 0.25/0.49
% 0.25/0.49 % Geq.prems(2)
% 0.25/0.49 thf(fact_6_usubstappt__plus__conv,axiom,
% 0.25/0.49 ! [Sigma: produc1418842292n_game,U: set_variable,Theta: trm,Eta: trm] :
% 0.25/0.49 ( ( ( uSubst516392818stappt @ Sigma @ U @ ( plus @ Theta @ Eta ) )
% 0.25/0.49 != none_trm )
% 0.25/0.49 => ( ( ( uSubst516392818stappt @ Sigma @ U @ Theta )
% 0.25/0.49 != none_trm )
% 0.25/0.49 & ( ( uSubst516392818stappt @ Sigma @ U @ Eta )
% 0.25/0.49 != none_trm ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % usubstappt_plus_conv
% 0.25/0.49 thf(fact_7_usubstappt__times__conv,axiom,
% 0.25/0.49 ! [Sigma: produc1418842292n_game,U: set_variable,Theta: trm,Eta: trm] :
% 0.25/0.49 ( ( ( uSubst516392818stappt @ Sigma @ U @ ( times @ Theta @ Eta ) )
% 0.25/0.49 != none_trm )
% 0.25/0.49 => ( ( ( uSubst516392818stappt @ Sigma @ U @ Theta )
% 0.25/0.49 != none_trm )
% 0.25/0.49 & ( ( uSubst516392818stappt @ Sigma @ U @ Eta )
% 0.25/0.49 != none_trm ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % usubstappt_times_conv
% 0.25/0.49 thf(fact_8_usubstappt__antimon,axiom,
% 0.25/0.49 ! [V: set_variable,U: set_variable,Sigma: produc1418842292n_game,Theta: trm] :
% 0.25/0.49 ( ( ord_le282106107riable @ V @ U )
% 0.25/0.49 => ( ( ( uSubst516392818stappt @ Sigma @ U @ Theta )
% 0.25/0.49 != none_trm )
% 0.25/0.49 => ( ( uSubst516392818stappt @ Sigma @ U @ Theta )
% 0.25/0.49 = ( uSubst516392818stappt @ Sigma @ V @ Theta ) ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % usubstappt_antimon
% 0.25/0.49 thf(fact_9_Differentialo_Osimps_I2_J,axiom,
% 0.25/0.49 ( ( uSubst716837505ntialo @ none_trm )
% 0.25/0.49 = none_trm ) ).
% 0.25/0.49
% 0.25/0.49 % Differentialo.simps(2)
% 0.25/0.49 thf(fact_10_Differentialo__undef,axiom,
% 0.25/0.49 ! [Theta: option_trm] :
% 0.25/0.49 ( ( ( uSubst716837505ntialo @ Theta )
% 0.25/0.49 = none_trm )
% 0.25/0.49 = ( Theta = none_trm ) ) ).
% 0.25/0.49
% 0.25/0.49 % Differentialo_undef
% 0.25/0.49 thf(fact_11_Pluso_Osimps_I2_J,axiom,
% 0.25/0.49 ! [Eta: option_trm] :
% 0.25/0.49 ( ( uSubst141955042_Pluso @ none_trm @ Eta )
% 0.25/0.49 = none_trm ) ).
% 0.25/0.49
% 0.25/0.49 % Pluso.simps(2)
% 0.25/0.49 thf(fact_12_Timeso_Osimps_I2_J,axiom,
% 0.25/0.49 ! [Eta: option_trm] :
% 0.25/0.49 ( ( uSubst918876924Timeso @ none_trm @ Eta )
% 0.25/0.49 = none_trm ) ).
% 0.25/0.49
% 0.25/0.49 % Timeso.simps(2)
% 0.25/0.49 thf(fact_13_Pluso__undef,axiom,
% 0.25/0.49 ! [Theta: option_trm,Eta: option_trm] :
% 0.25/0.49 ( ( ( uSubst141955042_Pluso @ Theta @ Eta )
% 0.25/0.49 = none_trm )
% 0.25/0.49 = ( ( Theta = none_trm )
% 0.25/0.49 | ( Eta = none_trm ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % Pluso_undef
% 0.25/0.49 thf(fact_14_Timeso__undef,axiom,
% 0.25/0.49 ! [Theta: option_trm,Eta: option_trm] :
% 0.25/0.49 ( ( ( uSubst918876924Timeso @ Theta @ Eta )
% 0.25/0.49 = none_trm )
% 0.25/0.49 = ( ( Theta = none_trm )
% 0.25/0.49 | ( Eta = none_trm ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % Timeso_undef
% 0.25/0.49 thf(fact_15_Geqo_Osimps_I2_J,axiom,
% 0.25/0.49 ! [Eta: option_trm] :
% 0.25/0.49 ( ( uSubst152838031e_Geqo @ none_trm @ Eta )
% 0.25/0.49 = none_fml ) ).
% 0.25/0.49
% 0.25/0.49 % Geqo.simps(2)
% 0.25/0.49 thf(fact_16_usubstappf__antimon,axiom,
% 0.25/0.49 ! [V: set_variable,U: set_variable,Sigma: produc1418842292n_game,Phi: fml] :
% 0.25/0.49 ( ( ord_le282106107riable @ V @ U )
% 0.25/0.49 => ( ( ( uSubst516392804stappf @ Sigma @ U @ Phi )
% 0.25/0.49 != none_fml )
% 0.25/0.49 => ( ( uSubst516392804stappf @ Sigma @ U @ Phi )
% 0.25/0.49 = ( uSubst516392804stappf @ Sigma @ V @ Phi ) ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % usubstappf_antimon
% 0.25/0.49 thf(fact_17_usubstappf__det,axiom,
% 0.25/0.49 ! [Sigma: produc1418842292n_game,U: set_variable,Phi: fml,V: set_variable] :
% 0.25/0.49 ( ( ( uSubst516392804stappf @ Sigma @ U @ Phi )
% 0.25/0.49 != none_fml )
% 0.25/0.49 => ( ( ( uSubst516392804stappf @ Sigma @ V @ Phi )
% 0.25/0.49 != none_fml )
% 0.25/0.49 => ( ( uSubst516392804stappf @ Sigma @ U @ Phi )
% 0.25/0.49 = ( uSubst516392804stappf @ Sigma @ V @ Phi ) ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % usubstappf_det
% 0.25/0.49 thf(fact_18_usubstappt_Osimps_I5_J,axiom,
% 0.25/0.49 ! [Sigma: produc1418842292n_game,U: set_variable,Theta: trm,Eta: trm] :
% 0.25/0.49 ( ( uSubst516392818stappt @ Sigma @ U @ ( plus @ Theta @ Eta ) )
% 0.25/0.49 = ( uSubst141955042_Pluso @ ( uSubst516392818stappt @ Sigma @ U @ Theta ) @ ( uSubst516392818stappt @ Sigma @ U @ Eta ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % usubstappt.simps(5)
% 0.25/0.49 thf(fact_19_usubstappt_Osimps_I6_J,axiom,
% 0.25/0.49 ! [Sigma: produc1418842292n_game,U: set_variable,Theta: trm,Eta: trm] :
% 0.25/0.49 ( ( uSubst516392818stappt @ Sigma @ U @ ( times @ Theta @ Eta ) )
% 0.25/0.49 = ( uSubst918876924Timeso @ ( uSubst516392818stappt @ Sigma @ U @ Theta ) @ ( uSubst516392818stappt @ Sigma @ U @ Eta ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % usubstappt.simps(6)
% 0.25/0.49 thf(fact_20_usubstappf_Osimps_I2_J,axiom,
% 0.25/0.49 ! [Sigma: produc1418842292n_game,U: set_variable,Theta: trm,Eta: trm] :
% 0.25/0.49 ( ( uSubst516392804stappf @ Sigma @ U @ ( geq @ Theta @ Eta ) )
% 0.25/0.49 = ( uSubst152838031e_Geqo @ ( uSubst516392818stappt @ Sigma @ U @ Theta ) @ ( uSubst516392818stappt @ Sigma @ U @ Eta ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % usubstappf.simps(2)
% 0.25/0.49 thf(fact_21_Geqo__undef,axiom,
% 0.25/0.49 ! [Theta: option_trm,Eta: option_trm] :
% 0.25/0.49 ( ( ( uSubst152838031e_Geqo @ Theta @ Eta )
% 0.25/0.49 = none_fml )
% 0.25/0.49 = ( ( Theta = none_trm )
% 0.25/0.49 | ( Eta = none_trm ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % Geqo_undef
% 0.25/0.49 thf(fact_22_trm_Oinject_I6_J,axiom,
% 0.25/0.49 ! [X61: trm,X62: trm,Y61: trm,Y62: trm] :
% 0.25/0.49 ( ( ( times @ X61 @ X62 )
% 0.25/0.49 = ( times @ Y61 @ Y62 ) )
% 0.25/0.49 = ( ( X61 = Y61 )
% 0.25/0.49 & ( X62 = Y62 ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % trm.inject(6)
% 0.25/0.49 thf(fact_23_trm_Oinject_I5_J,axiom,
% 0.25/0.49 ! [X51: trm,X52: trm,Y51: trm,Y52: trm] :
% 0.25/0.49 ( ( ( plus @ X51 @ X52 )
% 0.25/0.49 = ( plus @ Y51 @ Y52 ) )
% 0.25/0.49 = ( ( X51 = Y51 )
% 0.25/0.49 & ( X52 = Y52 ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % trm.inject(5)
% 0.25/0.49 thf(fact_24_fml_Oinject_I2_J,axiom,
% 0.25/0.49 ! [X21: trm,X22: trm,Y21: trm,Y22: trm] :
% 0.25/0.49 ( ( ( geq @ X21 @ X22 )
% 0.25/0.49 = ( geq @ Y21 @ Y22 ) )
% 0.25/0.49 = ( ( X21 = Y21 )
% 0.25/0.49 & ( X22 = Y22 ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % fml.inject(2)
% 0.25/0.49 thf(fact_25_Uvariation__mon,axiom,
% 0.25/0.49 ! [U: set_variable,V: set_variable,Omega: variable > real,Nu: variable > real] :
% 0.25/0.49 ( ( ord_le282106107riable @ U @ V )
% 0.25/0.49 => ( ( denota1419872369iation @ Omega @ Nu @ U )
% 0.25/0.49 => ( denota1419872369iation @ Omega @ Nu @ V ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % Uvariation_mon
% 0.25/0.49 thf(fact_26_subsetI,axiom,
% 0.25/0.49 ! [A: set_char,B: set_char] :
% 0.25/0.49 ( ! [X: char] :
% 0.25/0.49 ( ( member_char @ X @ A )
% 0.25/0.49 => ( member_char @ X @ B ) )
% 0.25/0.49 => ( ord_less_eq_set_char @ A @ B ) ) ).
% 0.25/0.49
% 0.25/0.49 % subsetI
% 0.25/0.49 thf(fact_27_subsetI,axiom,
% 0.25/0.49 ! [A: set_variable,B: set_variable] :
% 0.25/0.49 ( ! [X: variable] :
% 0.25/0.49 ( ( member_variable @ X @ A )
% 0.25/0.49 => ( member_variable @ X @ B ) )
% 0.25/0.49 => ( ord_le282106107riable @ A @ B ) ) ).
% 0.25/0.49
% 0.25/0.49 % subsetI
% 0.25/0.49 thf(fact_28_subset__antisym,axiom,
% 0.25/0.49 ! [A: set_variable,B: set_variable] :
% 0.25/0.49 ( ( ord_le282106107riable @ A @ B )
% 0.25/0.49 => ( ( ord_le282106107riable @ B @ A )
% 0.25/0.49 => ( A = B ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % subset_antisym
% 0.25/0.49 thf(fact_29_trm_Odistinct_I37_J,axiom,
% 0.25/0.49 ! [X51: trm,X52: trm,X61: trm,X62: trm] :
% 0.25/0.49 ( ( plus @ X51 @ X52 )
% 0.25/0.49 != ( times @ X61 @ X62 ) ) ).
% 0.25/0.49
% 0.25/0.49 % trm.distinct(37)
% 0.25/0.49 thf(fact_30_order__refl,axiom,
% 0.25/0.49 ! [X2: set_variable] : ( ord_le282106107riable @ X2 @ X2 ) ).
% 0.25/0.49
% 0.25/0.49 % order_refl
% 0.25/0.49 thf(fact_31_Uvariation__univ,axiom,
% 0.25/0.49 ! [Nu: variable > real,Nu2: variable > real] :
% 0.25/0.49 ( denota1419872369iation @ Nu @ Nu2
% 0.25/0.49 @ ( collect_variable
% 0.25/0.49 @ ^ [X3: variable] : $true ) ) ).
% 0.25/0.49
% 0.25/0.49 % Uvariation_univ
% 0.25/0.49 thf(fact_32_Collect__subset,axiom,
% 0.25/0.49 ! [A: set_char,P: char > $o] :
% 0.25/0.49 ( ord_less_eq_set_char
% 0.25/0.49 @ ( collect_char
% 0.25/0.49 @ ^ [X3: char] :
% 0.25/0.49 ( ( member_char @ X3 @ A )
% 0.25/0.49 & ( P @ X3 ) ) )
% 0.25/0.49 @ A ) ).
% 0.25/0.49
% 0.25/0.49 % Collect_subset
% 0.25/0.49 thf(fact_33_Collect__subset,axiom,
% 0.25/0.49 ! [A: set_variable,P: variable > $o] :
% 0.25/0.49 ( ord_le282106107riable
% 0.25/0.49 @ ( collect_variable
% 0.25/0.49 @ ^ [X3: variable] :
% 0.25/0.49 ( ( member_variable @ X3 @ A )
% 0.25/0.49 & ( P @ X3 ) ) )
% 0.25/0.49 @ A ) ).
% 0.25/0.49
% 0.25/0.49 % Collect_subset
% 0.25/0.49 thf(fact_34_less__eq__set__def,axiom,
% 0.25/0.49 ( ord_less_eq_set_char
% 0.25/0.49 = ( ^ [A2: set_char,B2: set_char] :
% 0.25/0.49 ( ord_less_eq_char_o
% 0.25/0.49 @ ^ [X3: char] : ( member_char @ X3 @ A2 )
% 0.25/0.49 @ ^ [X3: char] : ( member_char @ X3 @ B2 ) ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % less_eq_set_def
% 0.25/0.49 thf(fact_35_less__eq__set__def,axiom,
% 0.25/0.49 ( ord_le282106107riable
% 0.25/0.49 = ( ^ [A2: set_variable,B2: set_variable] :
% 0.25/0.49 ( ord_le1407353162able_o
% 0.25/0.49 @ ^ [X3: variable] : ( member_variable @ X3 @ A2 )
% 0.25/0.49 @ ^ [X3: variable] : ( member_variable @ X3 @ B2 ) ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % less_eq_set_def
% 0.25/0.49 thf(fact_36_dual__order_Oantisym,axiom,
% 0.25/0.49 ! [B3: set_variable,A3: set_variable] :
% 0.25/0.49 ( ( ord_le282106107riable @ B3 @ A3 )
% 0.25/0.49 => ( ( ord_le282106107riable @ A3 @ B3 )
% 0.25/0.49 => ( A3 = B3 ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % dual_order.antisym
% 0.25/0.49 thf(fact_37_dual__order_Oeq__iff,axiom,
% 0.25/0.49 ( ( ^ [Y: set_variable,Z: set_variable] : ( Y = Z ) )
% 0.25/0.49 = ( ^ [A4: set_variable,B4: set_variable] :
% 0.25/0.49 ( ( ord_le282106107riable @ B4 @ A4 )
% 0.25/0.49 & ( ord_le282106107riable @ A4 @ B4 ) ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % dual_order.eq_iff
% 0.25/0.49 thf(fact_38_dual__order_Otrans,axiom,
% 0.25/0.49 ! [B3: set_variable,A3: set_variable,C: set_variable] :
% 0.25/0.49 ( ( ord_le282106107riable @ B3 @ A3 )
% 0.25/0.49 => ( ( ord_le282106107riable @ C @ B3 )
% 0.25/0.49 => ( ord_le282106107riable @ C @ A3 ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % dual_order.trans
% 0.25/0.49 thf(fact_39_dual__order_Orefl,axiom,
% 0.25/0.49 ! [A3: set_variable] : ( ord_le282106107riable @ A3 @ A3 ) ).
% 0.25/0.49
% 0.25/0.49 % dual_order.refl
% 0.25/0.49 thf(fact_40_order__trans,axiom,
% 0.25/0.49 ! [X2: set_variable,Y2: set_variable,Z2: set_variable] :
% 0.25/0.49 ( ( ord_le282106107riable @ X2 @ Y2 )
% 0.25/0.49 => ( ( ord_le282106107riable @ Y2 @ Z2 )
% 0.25/0.49 => ( ord_le282106107riable @ X2 @ Z2 ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % order_trans
% 0.25/0.49 thf(fact_41_order__class_Oorder_Oantisym,axiom,
% 0.25/0.49 ! [A3: set_variable,B3: set_variable] :
% 0.25/0.49 ( ( ord_le282106107riable @ A3 @ B3 )
% 0.25/0.49 => ( ( ord_le282106107riable @ B3 @ A3 )
% 0.25/0.49 => ( A3 = B3 ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % order_class.order.antisym
% 0.25/0.49 thf(fact_42_ord__le__eq__trans,axiom,
% 0.25/0.49 ! [A3: set_variable,B3: set_variable,C: set_variable] :
% 0.25/0.49 ( ( ord_le282106107riable @ A3 @ B3 )
% 0.25/0.49 => ( ( B3 = C )
% 0.25/0.49 => ( ord_le282106107riable @ A3 @ C ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % ord_le_eq_trans
% 0.25/0.49 thf(fact_43_ord__eq__le__trans,axiom,
% 0.25/0.49 ! [A3: set_variable,B3: set_variable,C: set_variable] :
% 0.25/0.49 ( ( A3 = B3 )
% 0.25/0.49 => ( ( ord_le282106107riable @ B3 @ C )
% 0.25/0.49 => ( ord_le282106107riable @ A3 @ C ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % ord_eq_le_trans
% 0.25/0.49 thf(fact_44_order__class_Oorder_Oeq__iff,axiom,
% 0.25/0.49 ( ( ^ [Y: set_variable,Z: set_variable] : ( Y = Z ) )
% 0.25/0.49 = ( ^ [A4: set_variable,B4: set_variable] :
% 0.25/0.49 ( ( ord_le282106107riable @ A4 @ B4 )
% 0.25/0.49 & ( ord_le282106107riable @ B4 @ A4 ) ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % order_class.order.eq_iff
% 0.25/0.49 thf(fact_45_antisym__conv,axiom,
% 0.25/0.49 ! [Y2: set_variable,X2: set_variable] :
% 0.25/0.49 ( ( ord_le282106107riable @ Y2 @ X2 )
% 0.25/0.49 => ( ( ord_le282106107riable @ X2 @ Y2 )
% 0.25/0.49 = ( X2 = Y2 ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % antisym_conv
% 0.25/0.49 thf(fact_46_mem__Collect__eq,axiom,
% 0.25/0.49 ! [A3: variable,P: variable > $o] :
% 0.25/0.49 ( ( member_variable @ A3 @ ( collect_variable @ P ) )
% 0.25/0.49 = ( P @ A3 ) ) ).
% 0.25/0.49
% 0.25/0.49 % mem_Collect_eq
% 0.25/0.49 thf(fact_47_mem__Collect__eq,axiom,
% 0.25/0.49 ! [A3: char,P: char > $o] :
% 0.25/0.49 ( ( member_char @ A3 @ ( collect_char @ P ) )
% 0.25/0.49 = ( P @ A3 ) ) ).
% 0.25/0.49
% 0.25/0.49 % mem_Collect_eq
% 0.25/0.49 thf(fact_48_Collect__mem__eq,axiom,
% 0.25/0.49 ! [A: set_variable] :
% 0.25/0.49 ( ( collect_variable
% 0.25/0.49 @ ^ [X3: variable] : ( member_variable @ X3 @ A ) )
% 0.25/0.49 = A ) ).
% 0.25/0.49
% 0.25/0.49 % Collect_mem_eq
% 0.25/0.49 thf(fact_49_Collect__mem__eq,axiom,
% 0.25/0.49 ! [A: set_char] :
% 0.25/0.49 ( ( collect_char
% 0.25/0.49 @ ^ [X3: char] : ( member_char @ X3 @ A ) )
% 0.25/0.49 = A ) ).
% 0.25/0.49
% 0.25/0.49 % Collect_mem_eq
% 0.25/0.49 thf(fact_50_Collect__cong,axiom,
% 0.25/0.49 ! [P: variable > $o,Q: variable > $o] :
% 0.25/0.49 ( ! [X: variable] :
% 0.25/0.49 ( ( P @ X )
% 0.25/0.49 = ( Q @ X ) )
% 0.25/0.49 => ( ( collect_variable @ P )
% 0.25/0.49 = ( collect_variable @ Q ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % Collect_cong
% 0.25/0.49 thf(fact_51_Collect__cong,axiom,
% 0.25/0.49 ! [P: char > $o,Q: char > $o] :
% 0.25/0.49 ( ! [X: char] :
% 0.25/0.49 ( ( P @ X )
% 0.25/0.49 = ( Q @ X ) )
% 0.25/0.49 => ( ( collect_char @ P )
% 0.25/0.49 = ( collect_char @ Q ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % Collect_cong
% 0.25/0.49 thf(fact_52_order_Otrans,axiom,
% 0.25/0.49 ! [A3: set_variable,B3: set_variable,C: set_variable] :
% 0.25/0.49 ( ( ord_le282106107riable @ A3 @ B3 )
% 0.25/0.49 => ( ( ord_le282106107riable @ B3 @ C )
% 0.25/0.49 => ( ord_le282106107riable @ A3 @ C ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % order.trans
% 0.25/0.49 thf(fact_53_eq__refl,axiom,
% 0.25/0.49 ! [X2: set_variable,Y2: set_variable] :
% 0.25/0.49 ( ( X2 = Y2 )
% 0.25/0.49 => ( ord_le282106107riable @ X2 @ Y2 ) ) ).
% 0.25/0.49
% 0.25/0.49 % eq_refl
% 0.25/0.49 thf(fact_54_antisym,axiom,
% 0.25/0.49 ! [X2: set_variable,Y2: set_variable] :
% 0.25/0.49 ( ( ord_le282106107riable @ X2 @ Y2 )
% 0.25/0.49 => ( ( ord_le282106107riable @ Y2 @ X2 )
% 0.25/0.49 => ( X2 = Y2 ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % antisym
% 0.25/0.49 thf(fact_55_eq__iff,axiom,
% 0.25/0.49 ( ( ^ [Y: set_variable,Z: set_variable] : ( Y = Z ) )
% 0.25/0.49 = ( ^ [X3: set_variable,Y3: set_variable] :
% 0.25/0.49 ( ( ord_le282106107riable @ X3 @ Y3 )
% 0.25/0.49 & ( ord_le282106107riable @ Y3 @ X3 ) ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % eq_iff
% 0.25/0.49 thf(fact_56_ord__le__eq__subst,axiom,
% 0.25/0.49 ! [A3: set_variable,B3: set_variable,F: set_variable > set_variable,C: set_variable] :
% 0.25/0.49 ( ( ord_le282106107riable @ A3 @ B3 )
% 0.25/0.49 => ( ( ( F @ B3 )
% 0.25/0.49 = C )
% 0.25/0.49 => ( ! [X: set_variable,Y4: set_variable] :
% 0.25/0.49 ( ( ord_le282106107riable @ X @ Y4 )
% 0.25/0.49 => ( ord_le282106107riable @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.25/0.49 => ( ord_le282106107riable @ ( F @ A3 ) @ C ) ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % ord_le_eq_subst
% 0.25/0.49 thf(fact_57_ord__eq__le__subst,axiom,
% 0.25/0.49 ! [A3: set_variable,F: set_variable > set_variable,B3: set_variable,C: set_variable] :
% 0.25/0.49 ( ( A3
% 0.25/0.49 = ( F @ B3 ) )
% 0.25/0.49 => ( ( ord_le282106107riable @ B3 @ C )
% 0.25/0.49 => ( ! [X: set_variable,Y4: set_variable] :
% 0.25/0.49 ( ( ord_le282106107riable @ X @ Y4 )
% 0.25/0.49 => ( ord_le282106107riable @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.25/0.49 => ( ord_le282106107riable @ A3 @ ( F @ C ) ) ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % ord_eq_le_subst
% 0.25/0.49 thf(fact_58_order__subst2,axiom,
% 0.25/0.49 ! [A3: set_variable,B3: set_variable,F: set_variable > set_variable,C: set_variable] :
% 0.25/0.49 ( ( ord_le282106107riable @ A3 @ B3 )
% 0.25/0.49 => ( ( ord_le282106107riable @ ( F @ B3 ) @ C )
% 0.25/0.49 => ( ! [X: set_variable,Y4: set_variable] :
% 0.25/0.49 ( ( ord_le282106107riable @ X @ Y4 )
% 0.25/0.49 => ( ord_le282106107riable @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.25/0.49 => ( ord_le282106107riable @ ( F @ A3 ) @ C ) ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % order_subst2
% 0.25/0.49 thf(fact_59_order__subst1,axiom,
% 0.25/0.49 ! [A3: set_variable,F: set_variable > set_variable,B3: set_variable,C: set_variable] :
% 0.25/0.49 ( ( ord_le282106107riable @ A3 @ ( F @ B3 ) )
% 0.25/0.49 => ( ( ord_le282106107riable @ B3 @ C )
% 0.25/0.49 => ( ! [X: set_variable,Y4: set_variable] :
% 0.25/0.49 ( ( ord_le282106107riable @ X @ Y4 )
% 0.25/0.49 => ( ord_le282106107riable @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.25/0.49 => ( ord_le282106107riable @ A3 @ ( F @ C ) ) ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % order_subst1
% 0.25/0.49 thf(fact_60_Collect__mono__iff,axiom,
% 0.25/0.49 ! [P: char > $o,Q: char > $o] :
% 0.25/0.49 ( ( ord_less_eq_set_char @ ( collect_char @ P ) @ ( collect_char @ Q ) )
% 0.25/0.49 = ( ! [X3: char] :
% 0.25/0.49 ( ( P @ X3 )
% 0.25/0.49 => ( Q @ X3 ) ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % Collect_mono_iff
% 0.25/0.49 thf(fact_61_Collect__mono__iff,axiom,
% 0.25/0.49 ! [P: variable > $o,Q: variable > $o] :
% 0.25/0.49 ( ( ord_le282106107riable @ ( collect_variable @ P ) @ ( collect_variable @ Q ) )
% 0.25/0.49 = ( ! [X3: variable] :
% 0.25/0.49 ( ( P @ X3 )
% 0.25/0.49 => ( Q @ X3 ) ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % Collect_mono_iff
% 0.25/0.49 thf(fact_62_set__eq__subset,axiom,
% 0.25/0.49 ( ( ^ [Y: set_variable,Z: set_variable] : ( Y = Z ) )
% 0.25/0.49 = ( ^ [A2: set_variable,B2: set_variable] :
% 0.25/0.49 ( ( ord_le282106107riable @ A2 @ B2 )
% 0.25/0.49 & ( ord_le282106107riable @ B2 @ A2 ) ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % set_eq_subset
% 0.25/0.49 thf(fact_63_subset__trans,axiom,
% 0.25/0.49 ! [A: set_variable,B: set_variable,C2: set_variable] :
% 0.25/0.49 ( ( ord_le282106107riable @ A @ B )
% 0.25/0.49 => ( ( ord_le282106107riable @ B @ C2 )
% 0.25/0.49 => ( ord_le282106107riable @ A @ C2 ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % subset_trans
% 0.25/0.49 thf(fact_64_Collect__mono,axiom,
% 0.25/0.49 ! [P: char > $o,Q: char > $o] :
% 0.25/0.49 ( ! [X: char] :
% 0.25/0.49 ( ( P @ X )
% 0.25/0.49 => ( Q @ X ) )
% 0.25/0.49 => ( ord_less_eq_set_char @ ( collect_char @ P ) @ ( collect_char @ Q ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % Collect_mono
% 0.25/0.49 thf(fact_65_Collect__mono,axiom,
% 0.25/0.49 ! [P: variable > $o,Q: variable > $o] :
% 0.25/0.49 ( ! [X: variable] :
% 0.25/0.49 ( ( P @ X )
% 0.25/0.49 => ( Q @ X ) )
% 0.25/0.49 => ( ord_le282106107riable @ ( collect_variable @ P ) @ ( collect_variable @ Q ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % Collect_mono
% 0.25/0.49 thf(fact_66_subset__refl,axiom,
% 0.25/0.49 ! [A: set_variable] : ( ord_le282106107riable @ A @ A ) ).
% 0.25/0.49
% 0.25/0.49 % subset_refl
% 0.25/0.49 thf(fact_67_subset__iff,axiom,
% 0.25/0.49 ( ord_less_eq_set_char
% 0.25/0.49 = ( ^ [A2: set_char,B2: set_char] :
% 0.25/0.49 ! [T: char] :
% 0.25/0.49 ( ( member_char @ T @ A2 )
% 0.25/0.49 => ( member_char @ T @ B2 ) ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % subset_iff
% 0.25/0.49 thf(fact_68_subset__iff,axiom,
% 0.25/0.49 ( ord_le282106107riable
% 0.25/0.49 = ( ^ [A2: set_variable,B2: set_variable] :
% 0.25/0.49 ! [T: variable] :
% 0.25/0.49 ( ( member_variable @ T @ A2 )
% 0.25/0.49 => ( member_variable @ T @ B2 ) ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % subset_iff
% 0.25/0.49 thf(fact_69_equalityD2,axiom,
% 0.25/0.49 ! [A: set_variable,B: set_variable] :
% 0.25/0.49 ( ( A = B )
% 0.25/0.49 => ( ord_le282106107riable @ B @ A ) ) ).
% 0.25/0.49
% 0.25/0.49 % equalityD2
% 0.25/0.49 thf(fact_70_equalityD1,axiom,
% 0.25/0.49 ! [A: set_variable,B: set_variable] :
% 0.25/0.49 ( ( A = B )
% 0.25/0.49 => ( ord_le282106107riable @ A @ B ) ) ).
% 0.25/0.49
% 0.25/0.49 % equalityD1
% 0.25/0.49 thf(fact_71_subset__eq,axiom,
% 0.25/0.49 ( ord_less_eq_set_char
% 0.25/0.49 = ( ^ [A2: set_char,B2: set_char] :
% 0.25/0.49 ! [X3: char] :
% 0.25/0.49 ( ( member_char @ X3 @ A2 )
% 0.25/0.49 => ( member_char @ X3 @ B2 ) ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % subset_eq
% 0.25/0.49 thf(fact_72_subset__eq,axiom,
% 0.25/0.49 ( ord_le282106107riable
% 0.25/0.49 = ( ^ [A2: set_variable,B2: set_variable] :
% 0.25/0.49 ! [X3: variable] :
% 0.25/0.49 ( ( member_variable @ X3 @ A2 )
% 0.25/0.49 => ( member_variable @ X3 @ B2 ) ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % subset_eq
% 0.25/0.49 thf(fact_73_equalityE,axiom,
% 0.25/0.49 ! [A: set_variable,B: set_variable] :
% 0.25/0.49 ( ( A = B )
% 0.25/0.49 => ~ ( ( ord_le282106107riable @ A @ B )
% 0.25/0.49 => ~ ( ord_le282106107riable @ B @ A ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % equalityE
% 0.25/0.49 thf(fact_74_subsetD,axiom,
% 0.25/0.49 ! [A: set_char,B: set_char,C: char] :
% 0.25/0.49 ( ( ord_less_eq_set_char @ A @ B )
% 0.25/0.49 => ( ( member_char @ C @ A )
% 0.25/0.49 => ( member_char @ C @ B ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % subsetD
% 0.25/0.49 thf(fact_75_subsetD,axiom,
% 0.25/0.49 ! [A: set_variable,B: set_variable,C: variable] :
% 0.25/0.49 ( ( ord_le282106107riable @ A @ B )
% 0.25/0.49 => ( ( member_variable @ C @ A )
% 0.25/0.49 => ( member_variable @ C @ B ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % subsetD
% 0.25/0.49 thf(fact_76_in__mono,axiom,
% 0.25/0.49 ! [A: set_char,B: set_char,X2: char] :
% 0.25/0.49 ( ( ord_less_eq_set_char @ A @ B )
% 0.25/0.49 => ( ( member_char @ X2 @ A )
% 0.25/0.49 => ( member_char @ X2 @ B ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % in_mono
% 0.25/0.49 thf(fact_77_in__mono,axiom,
% 0.25/0.49 ! [A: set_variable,B: set_variable,X2: variable] :
% 0.25/0.49 ( ( ord_le282106107riable @ A @ B )
% 0.25/0.49 => ( ( member_variable @ X2 @ A )
% 0.25/0.49 => ( member_variable @ X2 @ B ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % in_mono
% 0.25/0.49 thf(fact_78_Uvariation__sym__rel,axiom,
% 0.25/0.49 ! [Omega: variable > real,Nu: variable > real,U: set_variable] :
% 0.25/0.49 ( ( denota1419872369iation @ Omega @ Nu @ U )
% 0.25/0.49 => ( denota1419872369iation @ Nu @ Omega @ U ) ) ).
% 0.25/0.49
% 0.25/0.49 % Uvariation_sym_rel
% 0.25/0.49 thf(fact_79_Uvariation__refl,axiom,
% 0.25/0.49 ! [Nu: variable > real,V: set_variable] : ( denota1419872369iation @ Nu @ Nu @ V ) ).
% 0.25/0.49
% 0.25/0.49 % Uvariation_refl
% 0.25/0.49 thf(fact_80_Uvariation__sym,axiom,
% 0.25/0.49 ( denota1419872369iation
% 0.25/0.49 = ( ^ [Omega2: variable > real,Nu3: variable > real] : ( denota1419872369iation @ Nu3 @ Omega2 ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % Uvariation_sym
% 0.25/0.49 thf(fact_81_Uvariation__def,axiom,
% 0.25/0.49 ( denota1419872369iation
% 0.25/0.49 = ( ^ [Nu3: variable > real,Nu4: variable > real,U2: set_variable] :
% 0.25/0.49 ! [I: variable] :
% 0.25/0.49 ( ~ ( member_variable @ I @ U2 )
% 0.25/0.49 => ( ( Nu3 @ I )
% 0.25/0.49 = ( Nu4 @ I ) ) ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % Uvariation_def
% 0.25/0.49 thf(fact_82_pred__subset__eq,axiom,
% 0.25/0.49 ! [R: set_char,S: set_char] :
% 0.25/0.49 ( ( ord_less_eq_char_o
% 0.25/0.49 @ ^ [X3: char] : ( member_char @ X3 @ R )
% 0.25/0.49 @ ^ [X3: char] : ( member_char @ X3 @ S ) )
% 0.25/0.49 = ( ord_less_eq_set_char @ R @ S ) ) ).
% 0.25/0.49
% 0.25/0.49 % pred_subset_eq
% 0.25/0.49 thf(fact_83_pred__subset__eq,axiom,
% 0.25/0.49 ! [R: set_variable,S: set_variable] :
% 0.25/0.49 ( ( ord_le1407353162able_o
% 0.25/0.49 @ ^ [X3: variable] : ( member_variable @ X3 @ R )
% 0.25/0.49 @ ^ [X3: variable] : ( member_variable @ X3 @ S ) )
% 0.25/0.49 = ( ord_le282106107riable @ R @ S ) ) ).
% 0.25/0.49
% 0.25/0.49 % pred_subset_eq
% 0.25/0.49 thf(fact_84_subset__Collect__iff,axiom,
% 0.25/0.49 ! [B: set_char,A: set_char,P: char > $o] :
% 0.25/0.49 ( ( ord_less_eq_set_char @ B @ A )
% 0.25/0.49 => ( ( ord_less_eq_set_char @ B
% 0.25/0.49 @ ( collect_char
% 0.25/0.49 @ ^ [X3: char] :
% 0.25/0.49 ( ( member_char @ X3 @ A )
% 0.25/0.49 & ( P @ X3 ) ) ) )
% 0.25/0.49 = ( ! [X3: char] :
% 0.25/0.49 ( ( member_char @ X3 @ B )
% 0.25/0.49 => ( P @ X3 ) ) ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % subset_Collect_iff
% 0.25/0.49 thf(fact_85_subset__Collect__iff,axiom,
% 0.25/0.49 ! [B: set_variable,A: set_variable,P: variable > $o] :
% 0.25/0.49 ( ( ord_le282106107riable @ B @ A )
% 0.25/0.49 => ( ( ord_le282106107riable @ B
% 0.25/0.49 @ ( collect_variable
% 0.25/0.49 @ ^ [X3: variable] :
% 0.25/0.49 ( ( member_variable @ X3 @ A )
% 0.25/0.49 & ( P @ X3 ) ) ) )
% 0.25/0.49 = ( ! [X3: variable] :
% 0.25/0.49 ( ( member_variable @ X3 @ B )
% 0.25/0.49 => ( P @ X3 ) ) ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % subset_Collect_iff
% 0.25/0.49 thf(fact_86_subset__CollectI,axiom,
% 0.25/0.49 ! [B: set_char,A: set_char,Q: char > $o,P: char > $o] :
% 0.25/0.49 ( ( ord_less_eq_set_char @ B @ A )
% 0.25/0.49 => ( ! [X: char] :
% 0.25/0.49 ( ( member_char @ X @ B )
% 0.25/0.49 => ( ( Q @ X )
% 0.25/0.49 => ( P @ X ) ) )
% 0.25/0.49 => ( ord_less_eq_set_char
% 0.25/0.49 @ ( collect_char
% 0.25/0.49 @ ^ [X3: char] :
% 0.25/0.49 ( ( member_char @ X3 @ B )
% 0.25/0.49 & ( Q @ X3 ) ) )
% 0.25/0.49 @ ( collect_char
% 0.25/0.49 @ ^ [X3: char] :
% 0.25/0.49 ( ( member_char @ X3 @ A )
% 0.25/0.49 & ( P @ X3 ) ) ) ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % subset_CollectI
% 0.25/0.49 thf(fact_87_subset__CollectI,axiom,
% 0.25/0.49 ! [B: set_variable,A: set_variable,Q: variable > $o,P: variable > $o] :
% 0.25/0.49 ( ( ord_le282106107riable @ B @ A )
% 0.25/0.49 => ( ! [X: variable] :
% 0.25/0.49 ( ( member_variable @ X @ B )
% 0.25/0.49 => ( ( Q @ X )
% 0.25/0.49 => ( P @ X ) ) )
% 0.25/0.49 => ( ord_le282106107riable
% 0.25/0.49 @ ( collect_variable
% 0.25/0.49 @ ^ [X3: variable] :
% 0.25/0.49 ( ( member_variable @ X3 @ B )
% 0.25/0.49 & ( Q @ X3 ) ) )
% 0.25/0.49 @ ( collect_variable
% 0.25/0.49 @ ^ [X3: variable] :
% 0.25/0.49 ( ( member_variable @ X3 @ A )
% 0.25/0.49 & ( P @ X3 ) ) ) ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % subset_CollectI
% 0.25/0.49 thf(fact_88_Collect__restrict,axiom,
% 0.25/0.49 ! [X4: set_char,P: char > $o] :
% 0.25/0.49 ( ord_less_eq_set_char
% 0.25/0.49 @ ( collect_char
% 0.25/0.49 @ ^ [X3: char] :
% 0.25/0.49 ( ( member_char @ X3 @ X4 )
% 0.25/0.49 & ( P @ X3 ) ) )
% 0.25/0.49 @ X4 ) ).
% 0.25/0.49
% 0.25/0.49 % Collect_restrict
% 0.25/0.49 thf(fact_89_Collect__restrict,axiom,
% 0.25/0.49 ! [X4: set_variable,P: variable > $o] :
% 0.25/0.49 ( ord_le282106107riable
% 0.25/0.49 @ ( collect_variable
% 0.25/0.49 @ ^ [X3: variable] :
% 0.25/0.49 ( ( member_variable @ X3 @ X4 )
% 0.25/0.49 & ( P @ X3 ) ) )
% 0.25/0.49 @ X4 ) ).
% 0.25/0.49
% 0.25/0.49 % Collect_restrict
% 0.25/0.49 thf(fact_90_prop__restrict,axiom,
% 0.25/0.49 ! [X2: char,Z3: set_char,X4: set_char,P: char > $o] :
% 0.25/0.49 ( ( member_char @ X2 @ Z3 )
% 0.25/0.49 => ( ( ord_less_eq_set_char @ Z3
% 0.25/0.49 @ ( collect_char
% 0.25/0.49 @ ^ [X3: char] :
% 0.25/0.49 ( ( member_char @ X3 @ X4 )
% 0.25/0.49 & ( P @ X3 ) ) ) )
% 0.25/0.49 => ( P @ X2 ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % prop_restrict
% 0.25/0.49 thf(fact_91_prop__restrict,axiom,
% 0.25/0.49 ! [X2: variable,Z3: set_variable,X4: set_variable,P: variable > $o] :
% 0.25/0.49 ( ( member_variable @ X2 @ Z3 )
% 0.25/0.49 => ( ( ord_le282106107riable @ Z3
% 0.25/0.49 @ ( collect_variable
% 0.25/0.49 @ ^ [X3: variable] :
% 0.25/0.49 ( ( member_variable @ X3 @ X4 )
% 0.25/0.49 & ( P @ X3 ) ) ) )
% 0.25/0.49 => ( P @ X2 ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % prop_restrict
% 0.25/0.49 thf(fact_92_conj__subset__def,axiom,
% 0.25/0.49 ! [A: set_char,P: char > $o,Q: char > $o] :
% 0.25/0.49 ( ( ord_less_eq_set_char @ A
% 0.25/0.49 @ ( collect_char
% 0.25/0.49 @ ^ [X3: char] :
% 0.25/0.49 ( ( P @ X3 )
% 0.25/0.49 & ( Q @ X3 ) ) ) )
% 0.25/0.49 = ( ( ord_less_eq_set_char @ A @ ( collect_char @ P ) )
% 0.25/0.49 & ( ord_less_eq_set_char @ A @ ( collect_char @ Q ) ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % conj_subset_def
% 0.25/0.49 thf(fact_93_conj__subset__def,axiom,
% 0.25/0.49 ! [A: set_variable,P: variable > $o,Q: variable > $o] :
% 0.25/0.49 ( ( ord_le282106107riable @ A
% 0.25/0.49 @ ( collect_variable
% 0.25/0.49 @ ^ [X3: variable] :
% 0.25/0.49 ( ( P @ X3 )
% 0.25/0.49 & ( Q @ X3 ) ) ) )
% 0.25/0.49 = ( ( ord_le282106107riable @ A @ ( collect_variable @ P ) )
% 0.25/0.49 & ( ord_le282106107riable @ A @ ( collect_variable @ Q ) ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % conj_subset_def
% 0.25/0.49 thf(fact_94_Pluso_Oelims,axiom,
% 0.25/0.49 ! [X2: option_trm,Xa: option_trm,Y2: option_trm] :
% 0.25/0.49 ( ( ( uSubst141955042_Pluso @ X2 @ Xa )
% 0.25/0.49 = Y2 )
% 0.25/0.49 => ( ! [Theta2: trm] :
% 0.25/0.49 ( ( X2
% 0.25/0.49 = ( some_trm @ Theta2 ) )
% 0.25/0.49 => ! [Eta2: trm] :
% 0.25/0.49 ( ( Xa
% 0.25/0.49 = ( some_trm @ Eta2 ) )
% 0.25/0.49 => ( Y2
% 0.25/0.49 != ( some_trm @ ( plus @ Theta2 @ Eta2 ) ) ) ) )
% 0.25/0.49 => ( ( ( X2 = none_trm )
% 0.25/0.49 => ( Y2 != none_trm ) )
% 0.25/0.49 => ~ ( ? [V2: trm] :
% 0.25/0.49 ( X2
% 0.25/0.49 = ( some_trm @ V2 ) )
% 0.25/0.49 => ( ( Xa = none_trm )
% 0.25/0.49 => ( Y2 != none_trm ) ) ) ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % Pluso.elims
% 0.25/0.49 thf(fact_95_Timeso_Oelims,axiom,
% 0.25/0.49 ! [X2: option_trm,Xa: option_trm,Y2: option_trm] :
% 0.25/0.49 ( ( ( uSubst918876924Timeso @ X2 @ Xa )
% 0.25/0.49 = Y2 )
% 0.25/0.49 => ( ! [Theta2: trm] :
% 0.25/0.49 ( ( X2
% 0.25/0.49 = ( some_trm @ Theta2 ) )
% 0.25/0.49 => ! [Eta2: trm] :
% 0.25/0.49 ( ( Xa
% 0.25/0.49 = ( some_trm @ Eta2 ) )
% 0.25/0.49 => ( Y2
% 0.25/0.49 != ( some_trm @ ( times @ Theta2 @ Eta2 ) ) ) ) )
% 0.25/0.49 => ( ( ( X2 = none_trm )
% 0.25/0.49 => ( Y2 != none_trm ) )
% 0.25/0.49 => ~ ( ? [V2: trm] :
% 0.25/0.49 ( X2
% 0.25/0.49 = ( some_trm @ V2 ) )
% 0.25/0.49 => ( ( Xa = none_trm )
% 0.25/0.49 => ( Y2 != none_trm ) ) ) ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % Timeso.elims
% 0.25/0.49 thf(fact_96_usubstappt_Osimps_I7_J,axiom,
% 0.25/0.49 ! [Sigma: produc1418842292n_game,U: set_variable,Theta: trm] :
% 0.25/0.49 ( ( uSubst516392818stappt @ Sigma @ U @ ( differential @ Theta ) )
% 0.25/0.49 = ( uSubst716837505ntialo
% 0.25/0.49 @ ( uSubst516392818stappt @ Sigma
% 0.25/0.49 @ ( collect_variable
% 0.25/0.49 @ ^ [X3: variable] : $true )
% 0.25/0.49 @ Theta ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % usubstappt.simps(7)
% 0.25/0.49 thf(fact_97_option_Oinject,axiom,
% 0.25/0.49 ! [X23: trm,Y23: trm] :
% 0.25/0.49 ( ( ( some_trm @ X23 )
% 0.25/0.49 = ( some_trm @ Y23 ) )
% 0.25/0.49 = ( X23 = Y23 ) ) ).
% 0.25/0.49
% 0.25/0.49 % option.inject
% 0.25/0.49 thf(fact_98_option_Oinject,axiom,
% 0.25/0.49 ! [X23: fml,Y23: fml] :
% 0.25/0.49 ( ( ( some_fml @ X23 )
% 0.25/0.49 = ( some_fml @ Y23 ) )
% 0.25/0.49 = ( X23 = Y23 ) ) ).
% 0.25/0.49
% 0.25/0.49 % option.inject
% 0.25/0.49 thf(fact_99_option_Oinject,axiom,
% 0.25/0.49 ! [X23: game,Y23: game] :
% 0.25/0.49 ( ( ( some_game @ X23 )
% 0.25/0.49 = ( some_game @ Y23 ) )
% 0.25/0.49 = ( X23 = Y23 ) ) ).
% 0.25/0.49
% 0.25/0.49 % option.inject
% 0.25/0.49 thf(fact_100_trm_Oinject_I7_J,axiom,
% 0.25/0.49 ! [X7: trm,Y7: trm] :
% 0.25/0.49 ( ( ( differential @ X7 )
% 0.25/0.49 = ( differential @ Y7 ) )
% 0.25/0.49 = ( X7 = Y7 ) ) ).
% 0.25/0.49
% 0.25/0.49 % trm.inject(7)
% 0.25/0.49 thf(fact_101_not__Some__eq,axiom,
% 0.25/0.49 ! [X2: option_trm] :
% 0.25/0.49 ( ( ! [Y3: trm] :
% 0.25/0.49 ( X2
% 0.25/0.49 != ( some_trm @ Y3 ) ) )
% 0.25/0.49 = ( X2 = none_trm ) ) ).
% 0.25/0.49
% 0.25/0.49 % not_Some_eq
% 0.25/0.49 thf(fact_102_not__Some__eq,axiom,
% 0.25/0.49 ! [X2: option_fml] :
% 0.25/0.49 ( ( ! [Y3: fml] :
% 0.25/0.49 ( X2
% 0.25/0.49 != ( some_fml @ Y3 ) ) )
% 0.25/0.49 = ( X2 = none_fml ) ) ).
% 0.25/0.49
% 0.25/0.49 % not_Some_eq
% 0.25/0.49 thf(fact_103_not__Some__eq,axiom,
% 0.25/0.49 ! [X2: option_game] :
% 0.25/0.49 ( ( ! [Y3: game] :
% 0.25/0.49 ( X2
% 0.25/0.49 != ( some_game @ Y3 ) ) )
% 0.25/0.49 = ( X2 = none_game ) ) ).
% 0.25/0.49
% 0.25/0.49 % not_Some_eq
% 0.25/0.49 thf(fact_104_not__None__eq,axiom,
% 0.25/0.49 ! [X2: option_trm] :
% 0.25/0.49 ( ( X2 != none_trm )
% 0.25/0.49 = ( ? [Y3: trm] :
% 0.25/0.49 ( X2
% 0.25/0.49 = ( some_trm @ Y3 ) ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % not_None_eq
% 0.25/0.49 thf(fact_105_not__None__eq,axiom,
% 0.25/0.49 ! [X2: option_fml] :
% 0.25/0.49 ( ( X2 != none_fml )
% 0.25/0.49 = ( ? [Y3: fml] :
% 0.25/0.49 ( X2
% 0.25/0.49 = ( some_fml @ Y3 ) ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % not_None_eq
% 0.25/0.49 thf(fact_106_not__None__eq,axiom,
% 0.25/0.49 ! [X2: option_game] :
% 0.25/0.49 ( ( X2 != none_game )
% 0.25/0.49 = ( ? [Y3: game] :
% 0.25/0.49 ( X2
% 0.25/0.49 = ( some_game @ Y3 ) ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % not_None_eq
% 0.25/0.49 thf(fact_107_Aterm__Some,axiom,
% 0.25/0.49 some_trm = some_trm ).
% 0.25/0.49
% 0.25/0.49 % Aterm_Some
% 0.25/0.49 thf(fact_108_Differentialo_Osimps_I1_J,axiom,
% 0.25/0.49 ! [Theta: trm] :
% 0.25/0.49 ( ( uSubst716837505ntialo @ ( some_trm @ Theta ) )
% 0.25/0.49 = ( some_trm @ ( differential @ Theta ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % Differentialo.simps(1)
% 0.25/0.49 thf(fact_109_combine__options__cases,axiom,
% 0.25/0.49 ! [X2: option_trm,P: option_trm > option_trm > $o,Y2: option_trm] :
% 0.25/0.49 ( ( ( X2 = none_trm )
% 0.25/0.49 => ( P @ X2 @ Y2 ) )
% 0.25/0.49 => ( ( ( Y2 = none_trm )
% 0.25/0.49 => ( P @ X2 @ Y2 ) )
% 0.25/0.49 => ( ! [A5: trm,B5: trm] :
% 0.25/0.49 ( ( X2
% 0.25/0.49 = ( some_trm @ A5 ) )
% 0.25/0.49 => ( ( Y2
% 0.25/0.49 = ( some_trm @ B5 ) )
% 0.25/0.49 => ( P @ X2 @ Y2 ) ) )
% 0.25/0.49 => ( P @ X2 @ Y2 ) ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % combine_options_cases
% 0.25/0.49 thf(fact_110_combine__options__cases,axiom,
% 0.25/0.49 ! [X2: option_trm,P: option_trm > option_fml > $o,Y2: option_fml] :
% 0.25/0.49 ( ( ( X2 = none_trm )
% 0.25/0.49 => ( P @ X2 @ Y2 ) )
% 0.25/0.49 => ( ( ( Y2 = none_fml )
% 0.25/0.49 => ( P @ X2 @ Y2 ) )
% 0.25/0.49 => ( ! [A5: trm,B5: fml] :
% 0.25/0.49 ( ( X2
% 0.25/0.49 = ( some_trm @ A5 ) )
% 0.25/0.49 => ( ( Y2
% 0.25/0.49 = ( some_fml @ B5 ) )
% 0.25/0.49 => ( P @ X2 @ Y2 ) ) )
% 0.25/0.49 => ( P @ X2 @ Y2 ) ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % combine_options_cases
% 0.25/0.49 thf(fact_111_combine__options__cases,axiom,
% 0.25/0.49 ! [X2: option_trm,P: option_trm > option_game > $o,Y2: option_game] :
% 0.25/0.49 ( ( ( X2 = none_trm )
% 0.25/0.49 => ( P @ X2 @ Y2 ) )
% 0.25/0.49 => ( ( ( Y2 = none_game )
% 0.25/0.49 => ( P @ X2 @ Y2 ) )
% 0.25/0.49 => ( ! [A5: trm,B5: game] :
% 0.25/0.49 ( ( X2
% 0.25/0.49 = ( some_trm @ A5 ) )
% 0.25/0.49 => ( ( Y2
% 0.25/0.49 = ( some_game @ B5 ) )
% 0.25/0.49 => ( P @ X2 @ Y2 ) ) )
% 0.25/0.49 => ( P @ X2 @ Y2 ) ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % combine_options_cases
% 0.25/0.49 thf(fact_112_combine__options__cases,axiom,
% 0.25/0.49 ! [X2: option_fml,P: option_fml > option_trm > $o,Y2: option_trm] :
% 0.25/0.49 ( ( ( X2 = none_fml )
% 0.25/0.49 => ( P @ X2 @ Y2 ) )
% 0.25/0.49 => ( ( ( Y2 = none_trm )
% 0.25/0.49 => ( P @ X2 @ Y2 ) )
% 0.25/0.49 => ( ! [A5: fml,B5: trm] :
% 0.25/0.49 ( ( X2
% 0.25/0.49 = ( some_fml @ A5 ) )
% 0.25/0.49 => ( ( Y2
% 0.25/0.49 = ( some_trm @ B5 ) )
% 0.25/0.49 => ( P @ X2 @ Y2 ) ) )
% 0.25/0.49 => ( P @ X2 @ Y2 ) ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % combine_options_cases
% 0.25/0.49 thf(fact_113_combine__options__cases,axiom,
% 0.25/0.49 ! [X2: option_fml,P: option_fml > option_fml > $o,Y2: option_fml] :
% 0.25/0.49 ( ( ( X2 = none_fml )
% 0.25/0.49 => ( P @ X2 @ Y2 ) )
% 0.25/0.49 => ( ( ( Y2 = none_fml )
% 0.25/0.49 => ( P @ X2 @ Y2 ) )
% 0.25/0.49 => ( ! [A5: fml,B5: fml] :
% 0.25/0.49 ( ( X2
% 0.25/0.49 = ( some_fml @ A5 ) )
% 0.25/0.49 => ( ( Y2
% 0.25/0.49 = ( some_fml @ B5 ) )
% 0.25/0.49 => ( P @ X2 @ Y2 ) ) )
% 0.25/0.49 => ( P @ X2 @ Y2 ) ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % combine_options_cases
% 0.25/0.49 thf(fact_114_combine__options__cases,axiom,
% 0.25/0.49 ! [X2: option_fml,P: option_fml > option_game > $o,Y2: option_game] :
% 0.25/0.49 ( ( ( X2 = none_fml )
% 0.25/0.49 => ( P @ X2 @ Y2 ) )
% 0.25/0.49 => ( ( ( Y2 = none_game )
% 0.25/0.49 => ( P @ X2 @ Y2 ) )
% 0.25/0.49 => ( ! [A5: fml,B5: game] :
% 0.25/0.49 ( ( X2
% 0.25/0.49 = ( some_fml @ A5 ) )
% 0.25/0.49 => ( ( Y2
% 0.25/0.49 = ( some_game @ B5 ) )
% 0.25/0.49 => ( P @ X2 @ Y2 ) ) )
% 0.25/0.49 => ( P @ X2 @ Y2 ) ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % combine_options_cases
% 0.25/0.49 thf(fact_115_combine__options__cases,axiom,
% 0.25/0.49 ! [X2: option_game,P: option_game > option_trm > $o,Y2: option_trm] :
% 0.25/0.49 ( ( ( X2 = none_game )
% 0.25/0.49 => ( P @ X2 @ Y2 ) )
% 0.25/0.49 => ( ( ( Y2 = none_trm )
% 0.25/0.49 => ( P @ X2 @ Y2 ) )
% 0.25/0.49 => ( ! [A5: game,B5: trm] :
% 0.25/0.49 ( ( X2
% 0.25/0.49 = ( some_game @ A5 ) )
% 0.25/0.49 => ( ( Y2
% 0.25/0.49 = ( some_trm @ B5 ) )
% 0.25/0.49 => ( P @ X2 @ Y2 ) ) )
% 0.25/0.49 => ( P @ X2 @ Y2 ) ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % combine_options_cases
% 0.25/0.49 thf(fact_116_combine__options__cases,axiom,
% 0.25/0.49 ! [X2: option_game,P: option_game > option_fml > $o,Y2: option_fml] :
% 0.25/0.49 ( ( ( X2 = none_game )
% 0.25/0.49 => ( P @ X2 @ Y2 ) )
% 0.25/0.49 => ( ( ( Y2 = none_fml )
% 0.25/0.49 => ( P @ X2 @ Y2 ) )
% 0.25/0.49 => ( ! [A5: game,B5: fml] :
% 0.25/0.49 ( ( X2
% 0.25/0.49 = ( some_game @ A5 ) )
% 0.25/0.49 => ( ( Y2
% 0.25/0.49 = ( some_fml @ B5 ) )
% 0.25/0.49 => ( P @ X2 @ Y2 ) ) )
% 0.25/0.49 => ( P @ X2 @ Y2 ) ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % combine_options_cases
% 0.25/0.49 thf(fact_117_combine__options__cases,axiom,
% 0.25/0.49 ! [X2: option_game,P: option_game > option_game > $o,Y2: option_game] :
% 0.25/0.49 ( ( ( X2 = none_game )
% 0.25/0.49 => ( P @ X2 @ Y2 ) )
% 0.25/0.49 => ( ( ( Y2 = none_game )
% 0.25/0.49 => ( P @ X2 @ Y2 ) )
% 0.25/0.49 => ( ! [A5: game,B5: game] :
% 0.25/0.49 ( ( X2
% 0.25/0.49 = ( some_game @ A5 ) )
% 0.25/0.49 => ( ( Y2
% 0.25/0.49 = ( some_game @ B5 ) )
% 0.25/0.49 => ( P @ X2 @ Y2 ) ) )
% 0.25/0.49 => ( P @ X2 @ Y2 ) ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % combine_options_cases
% 0.25/0.49 thf(fact_118_split__option__all,axiom,
% 0.25/0.49 ( ( ^ [P2: option_trm > $o] :
% 0.25/0.49 ! [X5: option_trm] : ( P2 @ X5 ) )
% 0.25/0.49 = ( ^ [P3: option_trm > $o] :
% 0.25/0.49 ( ( P3 @ none_trm )
% 0.25/0.49 & ! [X3: trm] : ( P3 @ ( some_trm @ X3 ) ) ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % split_option_all
% 0.25/0.49 thf(fact_119_split__option__all,axiom,
% 0.25/0.49 ( ( ^ [P2: option_fml > $o] :
% 0.25/0.49 ! [X5: option_fml] : ( P2 @ X5 ) )
% 0.25/0.49 = ( ^ [P3: option_fml > $o] :
% 0.25/0.49 ( ( P3 @ none_fml )
% 0.25/0.49 & ! [X3: fml] : ( P3 @ ( some_fml @ X3 ) ) ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % split_option_all
% 0.25/0.49 thf(fact_120_split__option__all,axiom,
% 0.25/0.49 ( ( ^ [P2: option_game > $o] :
% 0.25/0.49 ! [X5: option_game] : ( P2 @ X5 ) )
% 0.25/0.49 = ( ^ [P3: option_game > $o] :
% 0.25/0.49 ( ( P3 @ none_game )
% 0.25/0.49 & ! [X3: game] : ( P3 @ ( some_game @ X3 ) ) ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % split_option_all
% 0.25/0.49 thf(fact_121_split__option__ex,axiom,
% 0.25/0.49 ( ( ^ [P2: option_trm > $o] :
% 0.25/0.49 ? [X5: option_trm] : ( P2 @ X5 ) )
% 0.25/0.49 = ( ^ [P3: option_trm > $o] :
% 0.25/0.49 ( ( P3 @ none_trm )
% 0.25/0.49 | ? [X3: trm] : ( P3 @ ( some_trm @ X3 ) ) ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % split_option_ex
% 0.25/0.49 thf(fact_122_split__option__ex,axiom,
% 0.25/0.49 ( ( ^ [P2: option_fml > $o] :
% 0.25/0.49 ? [X5: option_fml] : ( P2 @ X5 ) )
% 0.25/0.49 = ( ^ [P3: option_fml > $o] :
% 0.25/0.49 ( ( P3 @ none_fml )
% 0.25/0.49 | ? [X3: fml] : ( P3 @ ( some_fml @ X3 ) ) ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % split_option_ex
% 0.25/0.49 thf(fact_123_split__option__ex,axiom,
% 0.25/0.49 ( ( ^ [P2: option_game > $o] :
% 0.25/0.49 ? [X5: option_game] : ( P2 @ X5 ) )
% 0.25/0.49 = ( ^ [P3: option_game > $o] :
% 0.25/0.49 ( ( P3 @ none_game )
% 0.25/0.49 | ? [X3: game] : ( P3 @ ( some_game @ X3 ) ) ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % split_option_ex
% 0.25/0.49 thf(fact_124_option_Oinducts,axiom,
% 0.25/0.49 ! [P: option_trm > $o,Option: option_trm] :
% 0.25/0.49 ( ( P @ none_trm )
% 0.25/0.49 => ( ! [X: trm] : ( P @ ( some_trm @ X ) )
% 0.25/0.49 => ( P @ Option ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % option.inducts
% 0.25/0.49 thf(fact_125_option_Oinducts,axiom,
% 0.25/0.49 ! [P: option_fml > $o,Option: option_fml] :
% 0.25/0.49 ( ( P @ none_fml )
% 0.25/0.49 => ( ! [X: fml] : ( P @ ( some_fml @ X ) )
% 0.25/0.49 => ( P @ Option ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % option.inducts
% 0.25/0.49 thf(fact_126_option_Oinducts,axiom,
% 0.25/0.49 ! [P: option_game > $o,Option: option_game] :
% 0.25/0.49 ( ( P @ none_game )
% 0.25/0.49 => ( ! [X: game] : ( P @ ( some_game @ X ) )
% 0.25/0.49 => ( P @ Option ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % option.inducts
% 0.25/0.49 thf(fact_127_option_Oexhaust,axiom,
% 0.25/0.49 ! [Y2: option_trm] :
% 0.25/0.49 ( ( Y2 != none_trm )
% 0.25/0.49 => ~ ! [X24: trm] :
% 0.25/0.49 ( Y2
% 0.25/0.49 != ( some_trm @ X24 ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % option.exhaust
% 0.25/0.49 thf(fact_128_option_Oexhaust,axiom,
% 0.25/0.49 ! [Y2: option_fml] :
% 0.25/0.49 ( ( Y2 != none_fml )
% 0.25/0.49 => ~ ! [X24: fml] :
% 0.25/0.49 ( Y2
% 0.25/0.49 != ( some_fml @ X24 ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % option.exhaust
% 0.25/0.49 thf(fact_129_option_Oexhaust,axiom,
% 0.25/0.49 ! [Y2: option_game] :
% 0.25/0.49 ( ( Y2 != none_game )
% 0.25/0.49 => ~ ! [X24: game] :
% 0.25/0.49 ( Y2
% 0.25/0.49 != ( some_game @ X24 ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % option.exhaust
% 0.25/0.49 thf(fact_130_option_OdiscI,axiom,
% 0.25/0.49 ! [Option: option_trm,X23: trm] :
% 0.25/0.49 ( ( Option
% 0.25/0.49 = ( some_trm @ X23 ) )
% 0.25/0.49 => ( Option != none_trm ) ) ).
% 0.25/0.49
% 0.25/0.49 % option.discI
% 0.25/0.49 thf(fact_131_option_OdiscI,axiom,
% 0.25/0.49 ! [Option: option_fml,X23: fml] :
% 0.25/0.49 ( ( Option
% 0.25/0.49 = ( some_fml @ X23 ) )
% 0.25/0.49 => ( Option != none_fml ) ) ).
% 0.25/0.49
% 0.25/0.49 % option.discI
% 0.25/0.49 thf(fact_132_option_OdiscI,axiom,
% 0.25/0.49 ! [Option: option_game,X23: game] :
% 0.25/0.49 ( ( Option
% 0.25/0.49 = ( some_game @ X23 ) )
% 0.25/0.49 => ( Option != none_game ) ) ).
% 0.25/0.49
% 0.25/0.49 % option.discI
% 0.25/0.49 thf(fact_133_option_Odistinct_I1_J,axiom,
% 0.25/0.49 ! [X23: trm] :
% 0.25/0.49 ( none_trm
% 0.25/0.49 != ( some_trm @ X23 ) ) ).
% 0.25/0.49
% 0.25/0.49 % option.distinct(1)
% 0.25/0.49 thf(fact_134_option_Odistinct_I1_J,axiom,
% 0.25/0.49 ! [X23: fml] :
% 0.25/0.49 ( none_fml
% 0.25/0.49 != ( some_fml @ X23 ) ) ).
% 0.25/0.49
% 0.25/0.49 % option.distinct(1)
% 0.25/0.49 thf(fact_135_option_Odistinct_I1_J,axiom,
% 0.25/0.49 ! [X23: game] :
% 0.25/0.49 ( none_game
% 0.25/0.49 != ( some_game @ X23 ) ) ).
% 0.25/0.49
% 0.25/0.49 % option.distinct(1)
% 0.25/0.49 thf(fact_136_Differentialo_Oinduct,axiom,
% 0.25/0.49 ! [P: option_trm > $o,A0: option_trm] :
% 0.25/0.49 ( ! [Theta2: trm] : ( P @ ( some_trm @ Theta2 ) )
% 0.25/0.49 => ( ( P @ none_trm )
% 0.25/0.49 => ( P @ A0 ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % Differentialo.induct
% 0.25/0.49 thf(fact_137_Differentialo_Ocases,axiom,
% 0.25/0.49 ! [X2: option_trm] :
% 0.25/0.49 ( ! [Theta2: trm] :
% 0.25/0.49 ( X2
% 0.25/0.49 != ( some_trm @ Theta2 ) )
% 0.25/0.49 => ( X2 = none_trm ) ) ).
% 0.25/0.49
% 0.25/0.49 % Differentialo.cases
% 0.25/0.49 thf(fact_138_Assigno_Oinduct,axiom,
% 0.25/0.49 ! [P: variable > option_trm > $o,A0: variable,A1: option_trm] :
% 0.25/0.49 ( ! [X: variable,Theta2: trm] : ( P @ X @ ( some_trm @ Theta2 ) )
% 0.25/0.49 => ( ! [X: variable] : ( P @ X @ none_trm )
% 0.25/0.49 => ( P @ A0 @ A1 ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % Assigno.induct
% 0.25/0.49 thf(fact_139_Timeso_Oinduct,axiom,
% 0.25/0.49 ! [P: option_trm > option_trm > $o,A0: option_trm,A1: option_trm] :
% 0.25/0.49 ( ! [Theta2: trm,Eta2: trm] : ( P @ ( some_trm @ Theta2 ) @ ( some_trm @ Eta2 ) )
% 0.25/0.49 => ( ! [X_1: option_trm] : ( P @ none_trm @ X_1 )
% 0.25/0.49 => ( ! [V2: trm] : ( P @ ( some_trm @ V2 ) @ none_trm )
% 0.25/0.49 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % Timeso.induct
% 0.25/0.49 thf(fact_140_undeft__equiv,axiom,
% 0.25/0.49 ! [Theta: option_trm] :
% 0.25/0.49 ( ( Theta != none_trm )
% 0.25/0.49 = ( ? [T: trm] :
% 0.25/0.49 ( Theta
% 0.25/0.49 = ( some_trm @ T ) ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % undeft_equiv
% 0.25/0.49 thf(fact_141_ODEo_Oinduct,axiom,
% 0.25/0.49 ! [P: char > option_trm > $o,A0: char,A1: option_trm] :
% 0.25/0.49 ( ! [X: char,Theta2: trm] : ( P @ X @ ( some_trm @ Theta2 ) )
% 0.25/0.49 => ( ! [X: char] : ( P @ X @ none_trm )
% 0.25/0.49 => ( P @ A0 @ A1 ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % ODEo.induct
% 0.25/0.49 thf(fact_142_Differentialo_Oelims,axiom,
% 0.25/0.49 ! [X2: option_trm,Y2: option_trm] :
% 0.25/0.49 ( ( ( uSubst716837505ntialo @ X2 )
% 0.25/0.49 = Y2 )
% 0.25/0.49 => ( ! [Theta2: trm] :
% 0.25/0.49 ( ( X2
% 0.25/0.49 = ( some_trm @ Theta2 ) )
% 0.25/0.49 => ( Y2
% 0.25/0.49 != ( some_trm @ ( differential @ Theta2 ) ) ) )
% 0.25/0.49 => ~ ( ( X2 = none_trm )
% 0.25/0.49 => ( Y2 != none_trm ) ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % Differentialo.elims
% 0.25/0.49 thf(fact_143_trm_Odistinct_I41_J,axiom,
% 0.25/0.49 ! [X61: trm,X62: trm,X7: trm] :
% 0.25/0.49 ( ( times @ X61 @ X62 )
% 0.25/0.49 != ( differential @ X7 ) ) ).
% 0.25/0.49
% 0.25/0.49 % trm.distinct(41)
% 0.25/0.49 thf(fact_144_trm_Odistinct_I39_J,axiom,
% 0.25/0.49 ! [X51: trm,X52: trm,X7: trm] :
% 0.25/0.49 ( ( plus @ X51 @ X52 )
% 0.25/0.49 != ( differential @ X7 ) ) ).
% 0.25/0.49
% 0.25/0.49 % trm.distinct(39)
% 0.25/0.49 thf(fact_145_Timeso_Osimps_I3_J,axiom,
% 0.25/0.49 ! [V3: trm] :
% 0.25/0.49 ( ( uSubst918876924Timeso @ ( some_trm @ V3 ) @ none_trm )
% 0.25/0.49 = none_trm ) ).
% 0.25/0.49
% 0.25/0.49 % Timeso.simps(3)
% 0.25/0.49 thf(fact_146_Pluso_Osimps_I3_J,axiom,
% 0.25/0.49 ! [V3: trm] :
% 0.25/0.49 ( ( uSubst141955042_Pluso @ ( some_trm @ V3 ) @ none_trm )
% 0.25/0.49 = none_trm ) ).
% 0.25/0.49
% 0.25/0.49 % Pluso.simps(3)
% 0.25/0.49 thf(fact_147_Pluso_Osimps_I1_J,axiom,
% 0.25/0.49 ! [Theta: trm,Eta: trm] :
% 0.25/0.49 ( ( uSubst141955042_Pluso @ ( some_trm @ Theta ) @ ( some_trm @ Eta ) )
% 0.25/0.49 = ( some_trm @ ( plus @ Theta @ Eta ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % Pluso.simps(1)
% 0.25/0.49 thf(fact_148_Timeso_Osimps_I1_J,axiom,
% 0.25/0.49 ! [Theta: trm,Eta: trm] :
% 0.25/0.49 ( ( uSubst918876924Timeso @ ( some_trm @ Theta ) @ ( some_trm @ Eta ) )
% 0.25/0.49 = ( some_trm @ ( times @ Theta @ Eta ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % Timeso.simps(1)
% 0.25/0.49 thf(fact_149_usubstappt__differential__conv,axiom,
% 0.25/0.49 ! [Sigma: produc1418842292n_game,U: set_variable,Theta: trm] :
% 0.25/0.49 ( ( ( uSubst516392818stappt @ Sigma @ U @ ( differential @ Theta ) )
% 0.25/0.49 != none_trm )
% 0.25/0.49 => ( ( uSubst516392818stappt @ Sigma
% 0.25/0.49 @ ( collect_variable
% 0.25/0.49 @ ^ [X3: variable] : $true )
% 0.25/0.49 @ Theta )
% 0.25/0.49 != none_trm ) ) ).
% 0.25/0.49
% 0.25/0.49 % usubstappt_differential_conv
% 0.25/0.49 thf(fact_150_Geqo_Osimps_I3_J,axiom,
% 0.25/0.49 ! [V3: trm] :
% 0.25/0.49 ( ( uSubst152838031e_Geqo @ ( some_trm @ V3 ) @ none_trm )
% 0.25/0.49 = none_fml ) ).
% 0.25/0.49
% 0.25/0.49 % Geqo.simps(3)
% 0.25/0.49 thf(fact_151_Geqo_Oelims,axiom,
% 0.25/0.49 ! [X2: option_trm,Xa: option_trm,Y2: option_fml] :
% 0.25/0.49 ( ( ( uSubst152838031e_Geqo @ X2 @ Xa )
% 0.25/0.49 = Y2 )
% 0.25/0.49 => ( ! [Theta2: trm] :
% 0.25/0.49 ( ( X2
% 0.25/0.49 = ( some_trm @ Theta2 ) )
% 0.25/0.49 => ! [Eta2: trm] :
% 0.25/0.49 ( ( Xa
% 0.25/0.49 = ( some_trm @ Eta2 ) )
% 0.25/0.49 => ( Y2
% 0.25/0.49 != ( some_fml @ ( geq @ Theta2 @ Eta2 ) ) ) ) )
% 0.25/0.49 => ( ( ( X2 = none_trm )
% 0.25/0.49 => ( Y2 != none_fml ) )
% 0.25/0.49 => ~ ( ? [V2: trm] :
% 0.25/0.49 ( X2
% 0.25/0.49 = ( some_trm @ V2 ) )
% 0.25/0.49 => ( ( Xa = none_trm )
% 0.25/0.49 => ( Y2 != none_fml ) ) ) ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % Geqo.elims
% 0.25/0.49 thf(fact_152_Differentialo_Opelims,axiom,
% 0.25/0.49 ! [X2: option_trm,Y2: option_trm] :
% 0.25/0.49 ( ( ( uSubst716837505ntialo @ X2 )
% 0.25/0.49 = Y2 )
% 0.25/0.49 => ( ( accp_option_trm @ uSubst2051024824lo_rel @ X2 )
% 0.25/0.49 => ( ! [Theta2: trm] :
% 0.25/0.49 ( ( X2
% 0.25/0.49 = ( some_trm @ Theta2 ) )
% 0.25/0.49 => ( ( Y2
% 0.25/0.49 = ( some_trm @ ( differential @ Theta2 ) ) )
% 0.25/0.49 => ~ ( accp_option_trm @ uSubst2051024824lo_rel @ ( some_trm @ Theta2 ) ) ) )
% 0.25/0.49 => ~ ( ( X2 = none_trm )
% 0.25/0.49 => ( ( Y2 = none_trm )
% 0.25/0.49 => ~ ( accp_option_trm @ uSubst2051024824lo_rel @ none_trm ) ) ) ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % Differentialo.pelims
% 0.25/0.49 thf(fact_153_Geqo_Osimps_I1_J,axiom,
% 0.25/0.49 ! [Theta: trm,Eta: trm] :
% 0.25/0.49 ( ( uSubst152838031e_Geqo @ ( some_trm @ Theta ) @ ( some_trm @ Eta ) )
% 0.25/0.49 = ( some_fml @ ( geq @ Theta @ Eta ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % Geqo.simps(1)
% 0.25/0.49 thf(fact_154_GreatestI2__order,axiom,
% 0.25/0.49 ! [P: set_variable > $o,X2: set_variable,Q: set_variable > $o] :
% 0.25/0.49 ( ( P @ X2 )
% 0.25/0.49 => ( ! [Y4: set_variable] :
% 0.25/0.49 ( ( P @ Y4 )
% 0.25/0.49 => ( ord_le282106107riable @ Y4 @ X2 ) )
% 0.25/0.49 => ( ! [X: set_variable] :
% 0.25/0.49 ( ( P @ X )
% 0.25/0.49 => ( ! [Y5: set_variable] :
% 0.25/0.49 ( ( P @ Y5 )
% 0.25/0.49 => ( ord_le282106107riable @ Y5 @ X ) )
% 0.25/0.49 => ( Q @ X ) ) )
% 0.25/0.49 => ( Q @ ( order_272405634riable @ P ) ) ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % GreatestI2_order
% 0.25/0.49 thf(fact_155_Greatest__equality,axiom,
% 0.25/0.49 ! [P: set_variable > $o,X2: set_variable] :
% 0.25/0.49 ( ( P @ X2 )
% 0.25/0.49 => ( ! [Y4: set_variable] :
% 0.25/0.49 ( ( P @ Y4 )
% 0.25/0.49 => ( ord_le282106107riable @ Y4 @ X2 ) )
% 0.25/0.49 => ( ( order_272405634riable @ P )
% 0.25/0.49 = X2 ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % Greatest_equality
% 0.25/0.49 thf(fact_156_Diamondo_Oinduct,axiom,
% 0.25/0.49 ! [P: option_game > option_fml > $o,A0: option_game,A1: option_fml] :
% 0.25/0.49 ( ! [Alpha: game,Phi2: fml] : ( P @ ( some_game @ Alpha ) @ ( some_fml @ Phi2 ) )
% 0.25/0.49 => ( ! [X_1: option_fml] : ( P @ none_game @ X_1 )
% 0.25/0.49 => ( ! [V2: game] : ( P @ ( some_game @ V2 ) @ none_fml )
% 0.25/0.49 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % Diamondo.induct
% 0.25/0.49 thf(fact_157_Existso_Oinduct,axiom,
% 0.25/0.49 ! [P: variable > option_fml > $o,A0: variable,A1: option_fml] :
% 0.25/0.49 ( ! [X: variable,Phi2: fml] : ( P @ X @ ( some_fml @ Phi2 ) )
% 0.25/0.49 => ( ! [X: variable] : ( P @ X @ none_fml )
% 0.25/0.49 => ( P @ A0 @ A1 ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % Existso.induct
% 0.25/0.49 thf(fact_158_undeff__equiv,axiom,
% 0.25/0.49 ! [Phi: option_fml] :
% 0.25/0.49 ( ( Phi != none_fml )
% 0.25/0.49 = ( ? [F2: fml] :
% 0.25/0.49 ( Phi
% 0.25/0.49 = ( some_fml @ F2 ) ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % undeff_equiv
% 0.25/0.49 thf(fact_159_Testo_Oinduct,axiom,
% 0.25/0.49 ! [P: option_fml > $o,A0: option_fml] :
% 0.25/0.49 ( ! [Phi2: fml] : ( P @ ( some_fml @ Phi2 ) )
% 0.25/0.49 => ( ( P @ none_fml )
% 0.25/0.49 => ( P @ A0 ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % Testo.induct
% 0.25/0.49 thf(fact_160_Testo_Ocases,axiom,
% 0.25/0.49 ! [X2: option_fml] :
% 0.25/0.49 ( ! [Phi2: fml] :
% 0.25/0.49 ( X2
% 0.25/0.49 != ( some_fml @ Phi2 ) )
% 0.25/0.49 => ( X2 = none_fml ) ) ).
% 0.25/0.49
% 0.25/0.49 % Testo.cases
% 0.25/0.49 thf(fact_161_Ando_Oinduct,axiom,
% 0.25/0.49 ! [P: option_fml > option_fml > $o,A0: option_fml,A1: option_fml] :
% 0.25/0.49 ( ! [Phi2: fml,Psi: fml] : ( P @ ( some_fml @ Phi2 ) @ ( some_fml @ Psi ) )
% 0.25/0.49 => ( ! [X_1: option_fml] : ( P @ none_fml @ X_1 )
% 0.25/0.49 => ( ! [V2: fml] : ( P @ ( some_fml @ V2 ) @ none_fml )
% 0.25/0.49 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % Ando.induct
% 0.25/0.49 thf(fact_162_accp__subset,axiom,
% 0.25/0.49 ! [R1: produc1024976764on_trm > produc1024976764on_trm > $o,R2: produc1024976764on_trm > produc1024976764on_trm > $o] :
% 0.25/0.49 ( ( ord_le370603054_trm_o @ R1 @ R2 )
% 0.25/0.49 => ( ord_le373274227_trm_o @ ( accp_P394694195on_trm @ R2 ) @ ( accp_P394694195on_trm @ R1 ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % accp_subset
% 0.25/0.49 thf(fact_163_accp__subset,axiom,
% 0.25/0.49 ! [R1: produc1072747943on_trm > produc1072747943on_trm > $o,R2: produc1072747943on_trm > produc1072747943on_trm > $o] :
% 0.25/0.49 ( ( ord_le90123726_trm_o @ R1 @ R2 )
% 0.25/0.49 => ( ord_le1721128566_trm_o @ ( accp_P758790320on_trm @ R2 ) @ ( accp_P758790320on_trm @ R1 ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % accp_subset
% 0.25/0.49 thf(fact_164_accp__subset,axiom,
% 0.25/0.49 ! [R1: produc464795408on_trm > produc464795408on_trm > $o,R2: produc464795408on_trm > produc464795408on_trm > $o] :
% 0.25/0.49 ( ( ord_le157637894_trm_o @ R1 @ R2 )
% 0.25/0.49 => ( ord_le1222882015_trm_o @ ( accp_P419951815on_trm @ R2 ) @ ( accp_P419951815on_trm @ R1 ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % accp_subset
% 0.25/0.49 thf(fact_165_accp__subset,axiom,
% 0.25/0.49 ! [R1: option_trm > option_trm > $o,R2: option_trm > option_trm > $o] :
% 0.25/0.49 ( ( ord_le847028878_trm_o @ R1 @ R2 )
% 0.25/0.49 => ( ord_le1957133745_trm_o @ ( accp_option_trm @ R2 ) @ ( accp_option_trm @ R1 ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % accp_subset
% 0.25/0.49 thf(fact_166_accp__subset,axiom,
% 0.25/0.49 ! [R1: option_fml > option_fml > $o,R2: option_fml > option_fml > $o] :
% 0.25/0.49 ( ( ord_le802833166_fml_o @ R1 @ R2 )
% 0.25/0.49 => ( ord_le181580155_fml_o @ ( accp_option_fml @ R2 ) @ ( accp_option_fml @ R1 ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % accp_subset
% 0.25/0.49 thf(fact_167_accp__subset__induct,axiom,
% 0.25/0.49 ! [D: produc1024976764on_trm > $o,R: produc1024976764on_trm > produc1024976764on_trm > $o,X2: produc1024976764on_trm,P: produc1024976764on_trm > $o] :
% 0.25/0.49 ( ( ord_le373274227_trm_o @ D @ ( accp_P394694195on_trm @ R ) )
% 0.25/0.49 => ( ! [X: produc1024976764on_trm,Z4: produc1024976764on_trm] :
% 0.25/0.49 ( ( D @ X )
% 0.25/0.49 => ( ( R @ Z4 @ X )
% 0.25/0.49 => ( D @ Z4 ) ) )
% 0.25/0.49 => ( ( D @ X2 )
% 0.25/0.49 => ( ! [X: produc1024976764on_trm] :
% 0.25/0.49 ( ( D @ X )
% 0.25/0.49 => ( ! [Z5: produc1024976764on_trm] :
% 0.25/0.49 ( ( R @ Z5 @ X )
% 0.25/0.49 => ( P @ Z5 ) )
% 0.25/0.49 => ( P @ X ) ) )
% 0.25/0.49 => ( P @ X2 ) ) ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % accp_subset_induct
% 0.25/0.49 thf(fact_168_accp__subset__induct,axiom,
% 0.25/0.49 ! [D: produc1072747943on_trm > $o,R: produc1072747943on_trm > produc1072747943on_trm > $o,X2: produc1072747943on_trm,P: produc1072747943on_trm > $o] :
% 0.25/0.49 ( ( ord_le1721128566_trm_o @ D @ ( accp_P758790320on_trm @ R ) )
% 0.25/0.49 => ( ! [X: produc1072747943on_trm,Z4: produc1072747943on_trm] :
% 0.25/0.49 ( ( D @ X )
% 0.25/0.49 => ( ( R @ Z4 @ X )
% 0.25/0.49 => ( D @ Z4 ) ) )
% 0.25/0.49 => ( ( D @ X2 )
% 0.25/0.49 => ( ! [X: produc1072747943on_trm] :
% 0.25/0.49 ( ( D @ X )
% 0.25/0.49 => ( ! [Z5: produc1072747943on_trm] :
% 0.25/0.49 ( ( R @ Z5 @ X )
% 0.25/0.49 => ( P @ Z5 ) )
% 0.25/0.49 => ( P @ X ) ) )
% 0.25/0.49 => ( P @ X2 ) ) ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % accp_subset_induct
% 0.25/0.49 thf(fact_169_accp__subset__induct,axiom,
% 0.25/0.49 ! [D: produc464795408on_trm > $o,R: produc464795408on_trm > produc464795408on_trm > $o,X2: produc464795408on_trm,P: produc464795408on_trm > $o] :
% 0.25/0.49 ( ( ord_le1222882015_trm_o @ D @ ( accp_P419951815on_trm @ R ) )
% 0.25/0.49 => ( ! [X: produc464795408on_trm,Z4: produc464795408on_trm] :
% 0.25/0.49 ( ( D @ X )
% 0.25/0.49 => ( ( R @ Z4 @ X )
% 0.25/0.49 => ( D @ Z4 ) ) )
% 0.25/0.49 => ( ( D @ X2 )
% 0.25/0.49 => ( ! [X: produc464795408on_trm] :
% 0.25/0.49 ( ( D @ X )
% 0.25/0.49 => ( ! [Z5: produc464795408on_trm] :
% 0.25/0.49 ( ( R @ Z5 @ X )
% 0.25/0.49 => ( P @ Z5 ) )
% 0.25/0.49 => ( P @ X ) ) )
% 0.25/0.49 => ( P @ X2 ) ) ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % accp_subset_induct
% 0.25/0.49 thf(fact_170_accp__subset__induct,axiom,
% 0.25/0.49 ! [D: option_trm > $o,R: option_trm > option_trm > $o,X2: option_trm,P: option_trm > $o] :
% 0.25/0.49 ( ( ord_le1957133745_trm_o @ D @ ( accp_option_trm @ R ) )
% 0.25/0.49 => ( ! [X: option_trm,Z4: option_trm] :
% 0.25/0.49 ( ( D @ X )
% 0.25/0.49 => ( ( R @ Z4 @ X )
% 0.25/0.49 => ( D @ Z4 ) ) )
% 0.25/0.49 => ( ( D @ X2 )
% 0.25/0.49 => ( ! [X: option_trm] :
% 0.25/0.49 ( ( D @ X )
% 0.25/0.49 => ( ! [Z5: option_trm] :
% 0.25/0.49 ( ( R @ Z5 @ X )
% 0.25/0.49 => ( P @ Z5 ) )
% 0.25/0.49 => ( P @ X ) ) )
% 0.25/0.49 => ( P @ X2 ) ) ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % accp_subset_induct
% 0.25/0.49 thf(fact_171_accp__subset__induct,axiom,
% 0.25/0.49 ! [D: option_fml > $o,R: option_fml > option_fml > $o,X2: option_fml,P: option_fml > $o] :
% 0.25/0.49 ( ( ord_le181580155_fml_o @ D @ ( accp_option_fml @ R ) )
% 0.25/0.49 => ( ! [X: option_fml,Z4: option_fml] :
% 0.25/0.49 ( ( D @ X )
% 0.25/0.49 => ( ( R @ Z4 @ X )
% 0.25/0.49 => ( D @ Z4 ) ) )
% 0.25/0.49 => ( ( D @ X2 )
% 0.25/0.49 => ( ! [X: option_fml] :
% 0.25/0.49 ( ( D @ X )
% 0.25/0.49 => ( ! [Z5: option_fml] :
% 0.25/0.49 ( ( R @ Z5 @ X )
% 0.25/0.49 => ( P @ Z5 ) )
% 0.25/0.49 => ( P @ X ) ) )
% 0.25/0.49 => ( P @ X2 ) ) ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % accp_subset_induct
% 0.25/0.49 thf(fact_172_usubstappf__geqr,axiom,
% 0.25/0.49 ! [Sigma: produc1418842292n_game,U: set_variable,Theta: trm,Eta: trm] :
% 0.25/0.49 ( ( ( uSubst516392804stappf @ Sigma @ U @ ( geq @ Theta @ Eta ) )
% 0.25/0.49 != none_fml )
% 0.25/0.49 => ( ( uSubst516392804stappf @ Sigma @ U @ ( geq @ Theta @ Eta ) )
% 0.25/0.49 = ( some_fml @ ( geq @ ( the_trm @ ( uSubst516392818stappt @ Sigma @ U @ Theta ) ) @ ( the_trm @ ( uSubst516392818stappt @ Sigma @ U @ Eta ) ) ) ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % usubstappf_geqr
% 0.25/0.49 thf(fact_173_usubstappf__geq,axiom,
% 0.25/0.49 ! [Sigma: produc1418842292n_game,U: set_variable,Theta: trm,Eta: trm] :
% 0.25/0.49 ( ( ( uSubst516392818stappt @ Sigma @ U @ Theta )
% 0.25/0.49 != none_trm )
% 0.25/0.49 => ( ( ( uSubst516392818stappt @ Sigma @ U @ Eta )
% 0.25/0.49 != none_trm )
% 0.25/0.49 => ( ( uSubst516392804stappf @ Sigma @ U @ ( geq @ Theta @ Eta ) )
% 0.25/0.49 = ( some_fml @ ( geq @ ( the_trm @ ( uSubst516392818stappt @ Sigma @ U @ Theta ) ) @ ( the_trm @ ( uSubst516392818stappt @ Sigma @ U @ Eta ) ) ) ) ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % usubstappf_geq
% 0.25/0.49 thf(fact_174_option_Ocollapse,axiom,
% 0.25/0.49 ! [Option: option_trm] :
% 0.25/0.49 ( ( Option != none_trm )
% 0.25/0.49 => ( ( some_trm @ ( the_trm @ Option ) )
% 0.25/0.49 = Option ) ) ).
% 0.25/0.49
% 0.25/0.49 % option.collapse
% 0.25/0.49 thf(fact_175_option_Ocollapse,axiom,
% 0.25/0.49 ! [Option: option_fml] :
% 0.25/0.49 ( ( Option != none_fml )
% 0.25/0.49 => ( ( some_fml @ ( the_fml @ Option ) )
% 0.25/0.49 = Option ) ) ).
% 0.25/0.49
% 0.25/0.49 % option.collapse
% 0.25/0.49 thf(fact_176_option_Ocollapse,axiom,
% 0.25/0.49 ! [Option: option_game] :
% 0.25/0.49 ( ( Option != none_game )
% 0.25/0.49 => ( ( some_game @ ( the_game @ Option ) )
% 0.25/0.49 = Option ) ) ).
% 0.25/0.49
% 0.25/0.49 % option.collapse
% 0.25/0.49 thf(fact_177_Composeo_Oinduct,axiom,
% 0.25/0.49 ! [P: option_game > option_game > $o,A0: option_game,A1: option_game] :
% 0.25/0.49 ( ! [Alpha: game,Beta: game] : ( P @ ( some_game @ Alpha ) @ ( some_game @ Beta ) )
% 0.25/0.49 => ( ! [Alpha: option_game] : ( P @ Alpha @ none_game )
% 0.25/0.49 => ( ! [V2: game] : ( P @ none_game @ ( some_game @ V2 ) )
% 0.25/0.49 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % Composeo.induct
% 0.25/0.49 thf(fact_178_undefg__equiv,axiom,
% 0.25/0.49 ! [Alpha2: option_game] :
% 0.25/0.49 ( ( Alpha2 != none_game )
% 0.25/0.49 = ( ? [G: game] :
% 0.25/0.49 ( Alpha2
% 0.25/0.49 = ( some_game @ G ) ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % undefg_equiv
% 0.25/0.49 thf(fact_179_Loopo_Oinduct,axiom,
% 0.25/0.49 ! [P: option_game > $o,A0: option_game] :
% 0.25/0.49 ( ! [Alpha: game] : ( P @ ( some_game @ Alpha ) )
% 0.25/0.49 => ( ( P @ none_game )
% 0.25/0.49 => ( P @ A0 ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % Loopo.induct
% 0.25/0.49 thf(fact_180_Loopo_Ocases,axiom,
% 0.25/0.49 ! [X2: option_game] :
% 0.25/0.49 ( ! [Alpha: game] :
% 0.25/0.49 ( X2
% 0.25/0.49 != ( some_game @ Alpha ) )
% 0.25/0.49 => ( X2 = none_game ) ) ).
% 0.25/0.49
% 0.25/0.49 % Loopo.cases
% 0.25/0.49 thf(fact_181_option_Oexpand,axiom,
% 0.25/0.49 ! [Option: option_trm,Option2: option_trm] :
% 0.25/0.49 ( ( ( Option = none_trm )
% 0.25/0.49 = ( Option2 = none_trm ) )
% 0.25/0.49 => ( ( ( Option != none_trm )
% 0.25/0.49 => ( ( Option2 != none_trm )
% 0.25/0.49 => ( ( the_trm @ Option )
% 0.25/0.49 = ( the_trm @ Option2 ) ) ) )
% 0.25/0.49 => ( Option = Option2 ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % option.expand
% 0.25/0.49 thf(fact_182_option_Oexpand,axiom,
% 0.25/0.49 ! [Option: option_fml,Option2: option_fml] :
% 0.25/0.49 ( ( ( Option = none_fml )
% 0.25/0.49 = ( Option2 = none_fml ) )
% 0.25/0.49 => ( ( ( Option != none_fml )
% 0.25/0.49 => ( ( Option2 != none_fml )
% 0.25/0.49 => ( ( the_fml @ Option )
% 0.25/0.49 = ( the_fml @ Option2 ) ) ) )
% 0.25/0.49 => ( Option = Option2 ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % option.expand
% 0.25/0.49 thf(fact_183_option_Oexpand,axiom,
% 0.25/0.49 ! [Option: option_game,Option2: option_game] :
% 0.25/0.49 ( ( ( Option = none_game )
% 0.25/0.49 = ( Option2 = none_game ) )
% 0.25/0.49 => ( ( ( Option != none_game )
% 0.25/0.49 => ( ( Option2 != none_game )
% 0.25/0.49 => ( ( the_game @ Option )
% 0.25/0.49 = ( the_game @ Option2 ) ) ) )
% 0.25/0.49 => ( Option = Option2 ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % option.expand
% 0.25/0.49 thf(fact_184_option_Osel,axiom,
% 0.25/0.49 ! [X23: trm] :
% 0.25/0.49 ( ( the_trm @ ( some_trm @ X23 ) )
% 0.25/0.49 = X23 ) ).
% 0.25/0.49
% 0.25/0.49 % option.sel
% 0.25/0.49 thf(fact_185_option_Osel,axiom,
% 0.25/0.49 ! [X23: fml] :
% 0.25/0.49 ( ( the_fml @ ( some_fml @ X23 ) )
% 0.25/0.49 = X23 ) ).
% 0.25/0.49
% 0.25/0.49 % option.sel
% 0.25/0.49 thf(fact_186_option_Osel,axiom,
% 0.25/0.49 ! [X23: game] :
% 0.25/0.49 ( ( the_game @ ( some_game @ X23 ) )
% 0.25/0.49 = X23 ) ).
% 0.25/0.49
% 0.25/0.49 % option.sel
% 0.25/0.49 thf(fact_187_option_Oexhaust__sel,axiom,
% 0.25/0.49 ! [Option: option_trm] :
% 0.25/0.49 ( ( Option != none_trm )
% 0.25/0.49 => ( Option
% 0.25/0.49 = ( some_trm @ ( the_trm @ Option ) ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % option.exhaust_sel
% 0.25/0.49 thf(fact_188_option_Oexhaust__sel,axiom,
% 0.25/0.49 ! [Option: option_fml] :
% 0.25/0.49 ( ( Option != none_fml )
% 0.25/0.49 => ( Option
% 0.25/0.49 = ( some_fml @ ( the_fml @ Option ) ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % option.exhaust_sel
% 0.25/0.49 thf(fact_189_option_Oexhaust__sel,axiom,
% 0.25/0.49 ! [Option: option_game] :
% 0.25/0.49 ( ( Option != none_game )
% 0.25/0.49 => ( Option
% 0.25/0.49 = ( some_game @ ( the_game @ Option ) ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % option.exhaust_sel
% 0.25/0.49 thf(fact_190_accp_Ocases,axiom,
% 0.25/0.49 ! [R3: produc1024976764on_trm > produc1024976764on_trm > $o,A3: produc1024976764on_trm] :
% 0.25/0.49 ( ( accp_P394694195on_trm @ R3 @ A3 )
% 0.25/0.49 => ! [Y5: produc1024976764on_trm] :
% 0.25/0.49 ( ( R3 @ Y5 @ A3 )
% 0.25/0.49 => ( accp_P394694195on_trm @ R3 @ Y5 ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % accp.cases
% 0.25/0.49 thf(fact_191_accp_Ocases,axiom,
% 0.25/0.49 ! [R3: produc1072747943on_trm > produc1072747943on_trm > $o,A3: produc1072747943on_trm] :
% 0.25/0.49 ( ( accp_P758790320on_trm @ R3 @ A3 )
% 0.25/0.49 => ! [Y5: produc1072747943on_trm] :
% 0.25/0.49 ( ( R3 @ Y5 @ A3 )
% 0.25/0.49 => ( accp_P758790320on_trm @ R3 @ Y5 ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % accp.cases
% 0.25/0.49 thf(fact_192_accp_Ocases,axiom,
% 0.25/0.49 ! [R3: produc464795408on_trm > produc464795408on_trm > $o,A3: produc464795408on_trm] :
% 0.25/0.49 ( ( accp_P419951815on_trm @ R3 @ A3 )
% 0.25/0.49 => ! [Y5: produc464795408on_trm] :
% 0.25/0.49 ( ( R3 @ Y5 @ A3 )
% 0.25/0.49 => ( accp_P419951815on_trm @ R3 @ Y5 ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % accp.cases
% 0.25/0.49 thf(fact_193_accp_Ocases,axiom,
% 0.25/0.49 ! [R3: option_trm > option_trm > $o,A3: option_trm] :
% 0.25/0.49 ( ( accp_option_trm @ R3 @ A3 )
% 0.25/0.49 => ! [Y5: option_trm] :
% 0.25/0.49 ( ( R3 @ Y5 @ A3 )
% 0.25/0.49 => ( accp_option_trm @ R3 @ Y5 ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % accp.cases
% 0.25/0.49 thf(fact_194_accp_Ocases,axiom,
% 0.25/0.49 ! [R3: option_fml > option_fml > $o,A3: option_fml] :
% 0.25/0.49 ( ( accp_option_fml @ R3 @ A3 )
% 0.25/0.49 => ! [Y5: option_fml] :
% 0.25/0.49 ( ( R3 @ Y5 @ A3 )
% 0.25/0.49 => ( accp_option_fml @ R3 @ Y5 ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % accp.cases
% 0.25/0.49 thf(fact_195_accp_Osimps,axiom,
% 0.25/0.49 ( accp_P394694195on_trm
% 0.25/0.49 = ( ^ [R4: produc1024976764on_trm > produc1024976764on_trm > $o,A4: produc1024976764on_trm] :
% 0.25/0.49 ? [X3: produc1024976764on_trm] :
% 0.25/0.49 ( ( A4 = X3 )
% 0.25/0.49 & ! [Y3: produc1024976764on_trm] :
% 0.25/0.49 ( ( R4 @ Y3 @ X3 )
% 0.25/0.49 => ( accp_P394694195on_trm @ R4 @ Y3 ) ) ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % accp.simps
% 0.25/0.49 thf(fact_196_accp_Osimps,axiom,
% 0.25/0.49 ( accp_P758790320on_trm
% 0.25/0.49 = ( ^ [R4: produc1072747943on_trm > produc1072747943on_trm > $o,A4: produc1072747943on_trm] :
% 0.25/0.49 ? [X3: produc1072747943on_trm] :
% 0.25/0.49 ( ( A4 = X3 )
% 0.25/0.49 & ! [Y3: produc1072747943on_trm] :
% 0.25/0.49 ( ( R4 @ Y3 @ X3 )
% 0.25/0.49 => ( accp_P758790320on_trm @ R4 @ Y3 ) ) ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % accp.simps
% 0.25/0.49 thf(fact_197_accp_Osimps,axiom,
% 0.25/0.49 ( accp_P419951815on_trm
% 0.25/0.49 = ( ^ [R4: produc464795408on_trm > produc464795408on_trm > $o,A4: produc464795408on_trm] :
% 0.25/0.49 ? [X3: produc464795408on_trm] :
% 0.25/0.49 ( ( A4 = X3 )
% 0.25/0.49 & ! [Y3: produc464795408on_trm] :
% 0.25/0.49 ( ( R4 @ Y3 @ X3 )
% 0.25/0.49 => ( accp_P419951815on_trm @ R4 @ Y3 ) ) ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % accp.simps
% 0.25/0.49 thf(fact_198_accp_Osimps,axiom,
% 0.25/0.49 ( accp_option_trm
% 0.25/0.49 = ( ^ [R4: option_trm > option_trm > $o,A4: option_trm] :
% 0.25/0.49 ? [X3: option_trm] :
% 0.25/0.49 ( ( A4 = X3 )
% 0.25/0.49 & ! [Y3: option_trm] :
% 0.25/0.49 ( ( R4 @ Y3 @ X3 )
% 0.25/0.49 => ( accp_option_trm @ R4 @ Y3 ) ) ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % accp.simps
% 0.25/0.49 thf(fact_199_accp_Osimps,axiom,
% 0.25/0.49 ( accp_option_fml
% 0.25/0.49 = ( ^ [R4: option_fml > option_fml > $o,A4: option_fml] :
% 0.25/0.49 ? [X3: option_fml] :
% 0.25/0.49 ( ( A4 = X3 )
% 0.25/0.49 & ! [Y3: option_fml] :
% 0.25/0.49 ( ( R4 @ Y3 @ X3 )
% 0.25/0.49 => ( accp_option_fml @ R4 @ Y3 ) ) ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % accp.simps
% 0.25/0.49 thf(fact_200_accp_Ointros,axiom,
% 0.25/0.49 ! [R3: produc1024976764on_trm > produc1024976764on_trm > $o,X2: produc1024976764on_trm] :
% 0.25/0.49 ( ! [Y4: produc1024976764on_trm] :
% 0.25/0.49 ( ( R3 @ Y4 @ X2 )
% 0.25/0.49 => ( accp_P394694195on_trm @ R3 @ Y4 ) )
% 0.25/0.49 => ( accp_P394694195on_trm @ R3 @ X2 ) ) ).
% 0.25/0.49
% 0.25/0.49 % accp.intros
% 0.25/0.49 thf(fact_201_accp_Ointros,axiom,
% 0.25/0.49 ! [R3: produc1072747943on_trm > produc1072747943on_trm > $o,X2: produc1072747943on_trm] :
% 0.25/0.49 ( ! [Y4: produc1072747943on_trm] :
% 0.25/0.49 ( ( R3 @ Y4 @ X2 )
% 0.25/0.49 => ( accp_P758790320on_trm @ R3 @ Y4 ) )
% 0.25/0.49 => ( accp_P758790320on_trm @ R3 @ X2 ) ) ).
% 0.25/0.49
% 0.25/0.49 % accp.intros
% 0.25/0.49 thf(fact_202_accp_Ointros,axiom,
% 0.25/0.49 ! [R3: produc464795408on_trm > produc464795408on_trm > $o,X2: produc464795408on_trm] :
% 0.25/0.49 ( ! [Y4: produc464795408on_trm] :
% 0.25/0.49 ( ( R3 @ Y4 @ X2 )
% 0.25/0.49 => ( accp_P419951815on_trm @ R3 @ Y4 ) )
% 0.25/0.49 => ( accp_P419951815on_trm @ R3 @ X2 ) ) ).
% 0.25/0.49
% 0.25/0.49 % accp.intros
% 0.25/0.49 thf(fact_203_accp_Ointros,axiom,
% 0.25/0.49 ! [R3: option_trm > option_trm > $o,X2: option_trm] :
% 0.25/0.49 ( ! [Y4: option_trm] :
% 0.25/0.49 ( ( R3 @ Y4 @ X2 )
% 0.25/0.49 => ( accp_option_trm @ R3 @ Y4 ) )
% 0.25/0.49 => ( accp_option_trm @ R3 @ X2 ) ) ).
% 0.25/0.49
% 0.25/0.49 % accp.intros
% 0.25/0.49 thf(fact_204_accp_Ointros,axiom,
% 0.25/0.49 ! [R3: option_fml > option_fml > $o,X2: option_fml] :
% 0.25/0.49 ( ! [Y4: option_fml] :
% 0.25/0.49 ( ( R3 @ Y4 @ X2 )
% 0.25/0.49 => ( accp_option_fml @ R3 @ Y4 ) )
% 0.25/0.49 => ( accp_option_fml @ R3 @ X2 ) ) ).
% 0.25/0.49
% 0.25/0.49 % accp.intros
% 0.25/0.49 thf(fact_205_accp__induct,axiom,
% 0.25/0.49 ! [R3: produc1024976764on_trm > produc1024976764on_trm > $o,A3: produc1024976764on_trm,P: produc1024976764on_trm > $o] :
% 0.25/0.49 ( ( accp_P394694195on_trm @ R3 @ A3 )
% 0.25/0.49 => ( ! [X: produc1024976764on_trm] :
% 0.25/0.49 ( ( accp_P394694195on_trm @ R3 @ X )
% 0.25/0.49 => ( ! [Y5: produc1024976764on_trm] :
% 0.25/0.49 ( ( R3 @ Y5 @ X )
% 0.25/0.49 => ( P @ Y5 ) )
% 0.25/0.49 => ( P @ X ) ) )
% 0.25/0.49 => ( P @ A3 ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % accp_induct
% 0.25/0.49 thf(fact_206_accp__induct,axiom,
% 0.25/0.49 ! [R3: produc1072747943on_trm > produc1072747943on_trm > $o,A3: produc1072747943on_trm,P: produc1072747943on_trm > $o] :
% 0.25/0.49 ( ( accp_P758790320on_trm @ R3 @ A3 )
% 0.25/0.49 => ( ! [X: produc1072747943on_trm] :
% 0.25/0.49 ( ( accp_P758790320on_trm @ R3 @ X )
% 0.25/0.49 => ( ! [Y5: produc1072747943on_trm] :
% 0.25/0.49 ( ( R3 @ Y5 @ X )
% 0.25/0.49 => ( P @ Y5 ) )
% 0.25/0.49 => ( P @ X ) ) )
% 0.25/0.49 => ( P @ A3 ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % accp_induct
% 0.25/0.49 thf(fact_207_accp__induct,axiom,
% 0.25/0.49 ! [R3: produc464795408on_trm > produc464795408on_trm > $o,A3: produc464795408on_trm,P: produc464795408on_trm > $o] :
% 0.25/0.49 ( ( accp_P419951815on_trm @ R3 @ A3 )
% 0.25/0.49 => ( ! [X: produc464795408on_trm] :
% 0.25/0.49 ( ( accp_P419951815on_trm @ R3 @ X )
% 0.25/0.49 => ( ! [Y5: produc464795408on_trm] :
% 0.25/0.49 ( ( R3 @ Y5 @ X )
% 0.25/0.49 => ( P @ Y5 ) )
% 0.25/0.49 => ( P @ X ) ) )
% 0.25/0.49 => ( P @ A3 ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % accp_induct
% 0.25/0.49 thf(fact_208_accp__induct,axiom,
% 0.25/0.49 ! [R3: option_trm > option_trm > $o,A3: option_trm,P: option_trm > $o] :
% 0.25/0.49 ( ( accp_option_trm @ R3 @ A3 )
% 0.25/0.49 => ( ! [X: option_trm] :
% 0.25/0.49 ( ( accp_option_trm @ R3 @ X )
% 0.25/0.49 => ( ! [Y5: option_trm] :
% 0.25/0.49 ( ( R3 @ Y5 @ X )
% 0.25/0.49 => ( P @ Y5 ) )
% 0.25/0.49 => ( P @ X ) ) )
% 0.25/0.49 => ( P @ A3 ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % accp_induct
% 0.25/0.49 thf(fact_209_accp__induct,axiom,
% 0.25/0.49 ! [R3: option_fml > option_fml > $o,A3: option_fml,P: option_fml > $o] :
% 0.25/0.49 ( ( accp_option_fml @ R3 @ A3 )
% 0.25/0.49 => ( ! [X: option_fml] :
% 0.25/0.49 ( ( accp_option_fml @ R3 @ X )
% 0.25/0.49 => ( ! [Y5: option_fml] :
% 0.25/0.49 ( ( R3 @ Y5 @ X )
% 0.25/0.49 => ( P @ Y5 ) )
% 0.25/0.49 => ( P @ X ) ) )
% 0.25/0.49 => ( P @ A3 ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % accp_induct
% 0.25/0.49 thf(fact_210_accp_Oinducts,axiom,
% 0.25/0.49 ! [R3: produc1024976764on_trm > produc1024976764on_trm > $o,X2: produc1024976764on_trm,P: produc1024976764on_trm > $o] :
% 0.25/0.49 ( ( accp_P394694195on_trm @ R3 @ X2 )
% 0.25/0.49 => ( ! [X: produc1024976764on_trm] :
% 0.25/0.49 ( ! [Y5: produc1024976764on_trm] :
% 0.25/0.49 ( ( R3 @ Y5 @ X )
% 0.25/0.49 => ( accp_P394694195on_trm @ R3 @ Y5 ) )
% 0.25/0.49 => ( ! [Y5: produc1024976764on_trm] :
% 0.25/0.49 ( ( R3 @ Y5 @ X )
% 0.25/0.49 => ( P @ Y5 ) )
% 0.25/0.49 => ( P @ X ) ) )
% 0.25/0.49 => ( P @ X2 ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % accp.inducts
% 0.25/0.49 thf(fact_211_accp_Oinducts,axiom,
% 0.25/0.49 ! [R3: produc1072747943on_trm > produc1072747943on_trm > $o,X2: produc1072747943on_trm,P: produc1072747943on_trm > $o] :
% 0.25/0.49 ( ( accp_P758790320on_trm @ R3 @ X2 )
% 0.25/0.49 => ( ! [X: produc1072747943on_trm] :
% 0.25/0.49 ( ! [Y5: produc1072747943on_trm] :
% 0.25/0.49 ( ( R3 @ Y5 @ X )
% 0.25/0.49 => ( accp_P758790320on_trm @ R3 @ Y5 ) )
% 0.25/0.49 => ( ! [Y5: produc1072747943on_trm] :
% 0.25/0.49 ( ( R3 @ Y5 @ X )
% 0.25/0.49 => ( P @ Y5 ) )
% 0.25/0.49 => ( P @ X ) ) )
% 0.25/0.49 => ( P @ X2 ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % accp.inducts
% 0.25/0.49 thf(fact_212_accp_Oinducts,axiom,
% 0.25/0.49 ! [R3: produc464795408on_trm > produc464795408on_trm > $o,X2: produc464795408on_trm,P: produc464795408on_trm > $o] :
% 0.25/0.49 ( ( accp_P419951815on_trm @ R3 @ X2 )
% 0.25/0.49 => ( ! [X: produc464795408on_trm] :
% 0.25/0.49 ( ! [Y5: produc464795408on_trm] :
% 0.25/0.49 ( ( R3 @ Y5 @ X )
% 0.25/0.49 => ( accp_P419951815on_trm @ R3 @ Y5 ) )
% 0.25/0.49 => ( ! [Y5: produc464795408on_trm] :
% 0.25/0.49 ( ( R3 @ Y5 @ X )
% 0.25/0.49 => ( P @ Y5 ) )
% 0.25/0.49 => ( P @ X ) ) )
% 0.25/0.49 => ( P @ X2 ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % accp.inducts
% 0.25/0.49 thf(fact_213_accp_Oinducts,axiom,
% 0.25/0.49 ! [R3: option_trm > option_trm > $o,X2: option_trm,P: option_trm > $o] :
% 0.25/0.49 ( ( accp_option_trm @ R3 @ X2 )
% 0.25/0.49 => ( ! [X: option_trm] :
% 0.25/0.49 ( ! [Y5: option_trm] :
% 0.25/0.49 ( ( R3 @ Y5 @ X )
% 0.25/0.49 => ( accp_option_trm @ R3 @ Y5 ) )
% 0.25/0.49 => ( ! [Y5: option_trm] :
% 0.25/0.49 ( ( R3 @ Y5 @ X )
% 0.25/0.49 => ( P @ Y5 ) )
% 0.25/0.49 => ( P @ X ) ) )
% 0.25/0.49 => ( P @ X2 ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % accp.inducts
% 0.25/0.49 thf(fact_214_accp_Oinducts,axiom,
% 0.25/0.49 ! [R3: option_fml > option_fml > $o,X2: option_fml,P: option_fml > $o] :
% 0.25/0.49 ( ( accp_option_fml @ R3 @ X2 )
% 0.25/0.49 => ( ! [X: option_fml] :
% 0.25/0.49 ( ! [Y5: option_fml] :
% 0.25/0.49 ( ( R3 @ Y5 @ X )
% 0.25/0.49 => ( accp_option_fml @ R3 @ Y5 ) )
% 0.25/0.49 => ( ! [Y5: option_fml] :
% 0.25/0.49 ( ( R3 @ Y5 @ X )
% 0.25/0.49 => ( P @ Y5 ) )
% 0.25/0.49 => ( P @ X ) ) )
% 0.25/0.49 => ( P @ X2 ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % accp.inducts
% 0.25/0.49 thf(fact_215_accp__downward,axiom,
% 0.25/0.49 ! [R3: produc1024976764on_trm > produc1024976764on_trm > $o,B3: produc1024976764on_trm,A3: produc1024976764on_trm] :
% 0.25/0.49 ( ( accp_P394694195on_trm @ R3 @ B3 )
% 0.25/0.49 => ( ( R3 @ A3 @ B3 )
% 0.25/0.49 => ( accp_P394694195on_trm @ R3 @ A3 ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % accp_downward
% 0.25/0.49 thf(fact_216_accp__downward,axiom,
% 0.25/0.49 ! [R3: produc1072747943on_trm > produc1072747943on_trm > $o,B3: produc1072747943on_trm,A3: produc1072747943on_trm] :
% 0.25/0.49 ( ( accp_P758790320on_trm @ R3 @ B3 )
% 0.25/0.49 => ( ( R3 @ A3 @ B3 )
% 0.25/0.49 => ( accp_P758790320on_trm @ R3 @ A3 ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % accp_downward
% 0.25/0.49 thf(fact_217_accp__downward,axiom,
% 0.25/0.49 ! [R3: produc464795408on_trm > produc464795408on_trm > $o,B3: produc464795408on_trm,A3: produc464795408on_trm] :
% 0.25/0.49 ( ( accp_P419951815on_trm @ R3 @ B3 )
% 0.25/0.49 => ( ( R3 @ A3 @ B3 )
% 0.25/0.49 => ( accp_P419951815on_trm @ R3 @ A3 ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % accp_downward
% 0.25/0.49 thf(fact_218_accp__downward,axiom,
% 0.25/0.49 ! [R3: option_trm > option_trm > $o,B3: option_trm,A3: option_trm] :
% 0.25/0.49 ( ( accp_option_trm @ R3 @ B3 )
% 0.25/0.49 => ( ( R3 @ A3 @ B3 )
% 0.25/0.49 => ( accp_option_trm @ R3 @ A3 ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % accp_downward
% 0.25/0.49 thf(fact_219_accp__downward,axiom,
% 0.25/0.49 ! [R3: option_fml > option_fml > $o,B3: option_fml,A3: option_fml] :
% 0.25/0.49 ( ( accp_option_fml @ R3 @ B3 )
% 0.25/0.49 => ( ( R3 @ A3 @ B3 )
% 0.25/0.49 => ( accp_option_fml @ R3 @ A3 ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % accp_downward
% 0.25/0.49 thf(fact_220_not__accp__down,axiom,
% 0.25/0.49 ! [R: produc1024976764on_trm > produc1024976764on_trm > $o,X2: produc1024976764on_trm] :
% 0.25/0.49 ( ~ ( accp_P394694195on_trm @ R @ X2 )
% 0.25/0.49 => ~ ! [Z4: produc1024976764on_trm] :
% 0.25/0.49 ( ( R @ Z4 @ X2 )
% 0.25/0.49 => ( accp_P394694195on_trm @ R @ Z4 ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % not_accp_down
% 0.25/0.49 thf(fact_221_not__accp__down,axiom,
% 0.25/0.49 ! [R: produc1072747943on_trm > produc1072747943on_trm > $o,X2: produc1072747943on_trm] :
% 0.25/0.49 ( ~ ( accp_P758790320on_trm @ R @ X2 )
% 0.25/0.49 => ~ ! [Z4: produc1072747943on_trm] :
% 0.25/0.49 ( ( R @ Z4 @ X2 )
% 0.25/0.49 => ( accp_P758790320on_trm @ R @ Z4 ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % not_accp_down
% 0.25/0.49 thf(fact_222_not__accp__down,axiom,
% 0.25/0.49 ! [R: produc464795408on_trm > produc464795408on_trm > $o,X2: produc464795408on_trm] :
% 0.25/0.49 ( ~ ( accp_P419951815on_trm @ R @ X2 )
% 0.25/0.49 => ~ ! [Z4: produc464795408on_trm] :
% 0.25/0.49 ( ( R @ Z4 @ X2 )
% 0.25/0.49 => ( accp_P419951815on_trm @ R @ Z4 ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % not_accp_down
% 0.25/0.49 thf(fact_223_not__accp__down,axiom,
% 0.25/0.49 ! [R: option_trm > option_trm > $o,X2: option_trm] :
% 0.25/0.49 ( ~ ( accp_option_trm @ R @ X2 )
% 0.25/0.49 => ~ ! [Z4: option_trm] :
% 0.25/0.49 ( ( R @ Z4 @ X2 )
% 0.25/0.49 => ( accp_option_trm @ R @ Z4 ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % not_accp_down
% 0.25/0.49 thf(fact_224_not__accp__down,axiom,
% 0.25/0.49 ! [R: option_fml > option_fml > $o,X2: option_fml] :
% 0.25/0.49 ( ~ ( accp_option_fml @ R @ X2 )
% 0.25/0.49 => ~ ! [Z4: option_fml] :
% 0.25/0.49 ( ( R @ Z4 @ X2 )
% 0.25/0.49 => ( accp_option_fml @ R @ Z4 ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % not_accp_down
% 0.25/0.49 thf(fact_225_accp__induct__rule,axiom,
% 0.25/0.49 ! [R3: produc1024976764on_trm > produc1024976764on_trm > $o,A3: produc1024976764on_trm,P: produc1024976764on_trm > $o] :
% 0.25/0.49 ( ( accp_P394694195on_trm @ R3 @ A3 )
% 0.25/0.49 => ( ! [X: produc1024976764on_trm] :
% 0.25/0.49 ( ( accp_P394694195on_trm @ R3 @ X )
% 0.25/0.49 => ( ! [Y5: produc1024976764on_trm] :
% 0.25/0.49 ( ( R3 @ Y5 @ X )
% 0.25/0.49 => ( P @ Y5 ) )
% 0.25/0.49 => ( P @ X ) ) )
% 0.25/0.49 => ( P @ A3 ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % accp_induct_rule
% 0.25/0.49 thf(fact_226_accp__induct__rule,axiom,
% 0.25/0.49 ! [R3: produc1072747943on_trm > produc1072747943on_trm > $o,A3: produc1072747943on_trm,P: produc1072747943on_trm > $o] :
% 0.25/0.49 ( ( accp_P758790320on_trm @ R3 @ A3 )
% 0.25/0.49 => ( ! [X: produc1072747943on_trm] :
% 0.25/0.49 ( ( accp_P758790320on_trm @ R3 @ X )
% 0.25/0.49 => ( ! [Y5: produc1072747943on_trm] :
% 0.25/0.49 ( ( R3 @ Y5 @ X )
% 0.25/0.49 => ( P @ Y5 ) )
% 0.25/0.49 => ( P @ X ) ) )
% 0.25/0.49 => ( P @ A3 ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % accp_induct_rule
% 0.25/0.49 thf(fact_227_accp__induct__rule,axiom,
% 0.25/0.49 ! [R3: produc464795408on_trm > produc464795408on_trm > $o,A3: produc464795408on_trm,P: produc464795408on_trm > $o] :
% 0.25/0.49 ( ( accp_P419951815on_trm @ R3 @ A3 )
% 0.25/0.49 => ( ! [X: produc464795408on_trm] :
% 0.25/0.49 ( ( accp_P419951815on_trm @ R3 @ X )
% 0.25/0.49 => ( ! [Y5: produc464795408on_trm] :
% 0.25/0.49 ( ( R3 @ Y5 @ X )
% 0.25/0.49 => ( P @ Y5 ) )
% 0.25/0.49 => ( P @ X ) ) )
% 0.25/0.49 => ( P @ A3 ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % accp_induct_rule
% 0.25/0.49 thf(fact_228_accp__induct__rule,axiom,
% 0.25/0.49 ! [R3: option_trm > option_trm > $o,A3: option_trm,P: option_trm > $o] :
% 0.25/0.49 ( ( accp_option_trm @ R3 @ A3 )
% 0.25/0.49 => ( ! [X: option_trm] :
% 0.25/0.49 ( ( accp_option_trm @ R3 @ X )
% 0.25/0.49 => ( ! [Y5: option_trm] :
% 0.25/0.49 ( ( R3 @ Y5 @ X )
% 0.25/0.49 => ( P @ Y5 ) )
% 0.25/0.49 => ( P @ X ) ) )
% 0.25/0.49 => ( P @ A3 ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % accp_induct_rule
% 0.25/0.49 thf(fact_229_accp__induct__rule,axiom,
% 0.25/0.49 ! [R3: option_fml > option_fml > $o,A3: option_fml,P: option_fml > $o] :
% 0.25/0.49 ( ( accp_option_fml @ R3 @ A3 )
% 0.25/0.49 => ( ! [X: option_fml] :
% 0.25/0.49 ( ( accp_option_fml @ R3 @ X )
% 0.25/0.49 => ( ! [Y5: option_fml] :
% 0.25/0.49 ( ( R3 @ Y5 @ X )
% 0.25/0.49 => ( P @ Y5 ) )
% 0.25/0.49 => ( P @ X ) ) )
% 0.25/0.49 => ( P @ A3 ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % accp_induct_rule
% 0.25/0.49 thf(fact_230_Geqo_Opelims,axiom,
% 0.25/0.49 ! [X2: option_trm,Xa: option_trm,Y2: option_fml] :
% 0.25/0.49 ( ( ( uSubst152838031e_Geqo @ X2 @ Xa )
% 0.25/0.49 = Y2 )
% 0.25/0.49 => ( ( accp_P758790320on_trm @ uSubst1304144938qo_rel @ ( produc709594775on_trm @ X2 @ Xa ) )
% 0.25/0.49 => ( ! [Theta2: trm] :
% 0.25/0.49 ( ( X2
% 0.25/0.49 = ( some_trm @ Theta2 ) )
% 0.25/0.49 => ! [Eta2: trm] :
% 0.25/0.49 ( ( Xa
% 0.25/0.49 = ( some_trm @ Eta2 ) )
% 0.25/0.49 => ( ( Y2
% 0.25/0.49 = ( some_fml @ ( geq @ Theta2 @ Eta2 ) ) )
% 0.25/0.49 => ~ ( accp_P758790320on_trm @ uSubst1304144938qo_rel @ ( produc709594775on_trm @ ( some_trm @ Theta2 ) @ ( some_trm @ Eta2 ) ) ) ) ) )
% 0.25/0.49 => ( ( ( X2 = none_trm )
% 0.25/0.49 => ( ( Y2 = none_fml )
% 0.25/0.49 => ~ ( accp_P758790320on_trm @ uSubst1304144938qo_rel @ ( produc709594775on_trm @ none_trm @ Xa ) ) ) )
% 0.25/0.49 => ~ ! [V2: trm] :
% 0.25/0.49 ( ( X2
% 0.25/0.49 = ( some_trm @ V2 ) )
% 0.25/0.49 => ( ( Xa = none_trm )
% 0.25/0.49 => ( ( Y2 = none_fml )
% 0.25/0.49 => ~ ( accp_P758790320on_trm @ uSubst1304144938qo_rel @ ( produc709594775on_trm @ ( some_trm @ V2 ) @ none_trm ) ) ) ) ) ) ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % Geqo.pelims
% 0.25/0.49 thf(fact_231_Diamondo_Ocases,axiom,
% 0.25/0.49 ! [X2: produc1739631244on_fml] :
% 0.25/0.49 ( ! [Alpha: game,Phi2: fml] :
% 0.25/0.49 ( X2
% 0.25/0.49 != ( produc2124676926on_fml @ ( some_game @ Alpha ) @ ( some_fml @ Phi2 ) ) )
% 0.25/0.49 => ( ! [Phi2: option_fml] :
% 0.25/0.49 ( X2
% 0.25/0.49 != ( produc2124676926on_fml @ none_game @ Phi2 ) )
% 0.25/0.49 => ~ ! [V2: game] :
% 0.25/0.49 ( X2
% 0.25/0.49 != ( produc2124676926on_fml @ ( some_game @ V2 ) @ none_fml ) ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % Diamondo.cases
% 0.25/0.49 thf(fact_232_subrelI,axiom,
% 0.25/0.49 ! [R3: set_Pr622314946on_fml,S2: set_Pr622314946on_fml] :
% 0.25/0.49 ( ! [X: option_game,Y4: option_fml] :
% 0.25/0.49 ( ( member1883102883on_fml @ ( produc2124676926on_fml @ X @ Y4 ) @ R3 )
% 0.25/0.49 => ( member1883102883on_fml @ ( produc2124676926on_fml @ X @ Y4 ) @ S2 ) )
% 0.25/0.49 => ( ord_le782333474on_fml @ R3 @ S2 ) ) ).
% 0.25/0.49
% 0.25/0.49 % subrelI
% 0.25/0.49 thf(fact_233_subrelI,axiom,
% 0.25/0.49 ! [R3: set_Pr1471344007on_trm,S2: set_Pr1471344007on_trm] :
% 0.25/0.49 ( ! [X: option_trm,Y4: option_trm] :
% 0.25/0.49 ( ( member165817296on_trm @ ( produc709594775on_trm @ X @ Y4 ) @ R3 )
% 0.25/0.49 => ( member165817296on_trm @ ( produc709594775on_trm @ X @ Y4 ) @ S2 ) )
% 0.25/0.49 => ( ord_le1322722599on_trm @ R3 @ S2 ) ) ).
% 0.25/0.49
% 0.25/0.49 % subrelI
% 0.25/0.49 thf(fact_234_subrelI,axiom,
% 0.25/0.49 ! [R3: set_Pr927595527on_fml,S2: set_Pr927595527on_fml] :
% 0.25/0.49 ( ! [X: option_fml,Y4: option_fml] :
% 0.25/0.49 ( ( member1287158352on_fml @ ( produc909629463on_fml @ X @ Y4 ) @ R3 )
% 0.25/0.49 => ( member1287158352on_fml @ ( produc909629463on_fml @ X @ Y4 ) @ S2 ) )
% 0.25/0.49 => ( ord_le778974119on_fml @ R3 @ S2 ) ) ).
% 0.25/0.49
% 0.25/0.49 % subrelI
% 0.25/0.49 thf(fact_235_subrelI,axiom,
% 0.25/0.49 ! [R3: set_Pr943832262on_trm,S2: set_Pr943832262on_trm] :
% 0.25/0.49 ( ! [X: char,Y4: option_trm] :
% 0.25/0.49 ( ( member694524327on_trm @ ( produc1500300866on_trm @ X @ Y4 ) @ R3 )
% 0.25/0.49 => ( member694524327on_trm @ ( produc1500300866on_trm @ X @ Y4 ) @ S2 ) )
% 0.25/0.49 => ( ord_le541293862on_trm @ R3 @ S2 ) ) ).
% 0.25/0.49
% 0.25/0.49 % subrelI
% 0.25/0.49 thf(fact_236_subrelI,axiom,
% 0.25/0.49 ! [R3: set_Pr1235432374le_trm,S2: set_Pr1235432374le_trm] :
% 0.25/0.49 ( ! [X: set_variable,Y4: trm] :
% 0.25/0.49 ( ( member2122665623le_trm @ ( produc1482344242le_trm @ X @ Y4 ) @ R3 )
% 0.25/0.49 => ( member2122665623le_trm @ ( produc1482344242le_trm @ X @ Y4 ) @ S2 ) )
% 0.25/0.49 => ( ord_le2102862870le_trm @ R3 @ S2 ) ) ).
% 0.25/0.49
% 0.25/0.49 % subrelI
% 0.25/0.49 thf(fact_237_ssubst__Pair__rhs,axiom,
% 0.25/0.49 ! [R3: option_game,S2: option_fml,R: set_Pr622314946on_fml,S3: option_fml] :
% 0.25/0.49 ( ( member1883102883on_fml @ ( produc2124676926on_fml @ R3 @ S2 ) @ R )
% 0.25/0.49 => ( ( S3 = S2 )
% 0.25/0.49 => ( member1883102883on_fml @ ( produc2124676926on_fml @ R3 @ S3 ) @ R ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % ssubst_Pair_rhs
% 0.25/0.49 thf(fact_238_ssubst__Pair__rhs,axiom,
% 0.25/0.49 ! [R3: option_trm,S2: option_trm,R: set_Pr1471344007on_trm,S3: option_trm] :
% 0.25/0.49 ( ( member165817296on_trm @ ( produc709594775on_trm @ R3 @ S2 ) @ R )
% 0.25/0.49 => ( ( S3 = S2 )
% 0.25/0.49 => ( member165817296on_trm @ ( produc709594775on_trm @ R3 @ S3 ) @ R ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % ssubst_Pair_rhs
% 0.25/0.49 thf(fact_239_ssubst__Pair__rhs,axiom,
% 0.25/0.49 ! [R3: option_fml,S2: option_fml,R: set_Pr927595527on_fml,S3: option_fml] :
% 0.25/0.49 ( ( member1287158352on_fml @ ( produc909629463on_fml @ R3 @ S2 ) @ R )
% 0.25/0.49 => ( ( S3 = S2 )
% 0.25/0.49 => ( member1287158352on_fml @ ( produc909629463on_fml @ R3 @ S3 ) @ R ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % ssubst_Pair_rhs
% 0.25/0.49 thf(fact_240_ssubst__Pair__rhs,axiom,
% 0.25/0.49 ! [R3: char,S2: option_trm,R: set_Pr943832262on_trm,S3: option_trm] :
% 0.25/0.49 ( ( member694524327on_trm @ ( produc1500300866on_trm @ R3 @ S2 ) @ R )
% 0.25/0.49 => ( ( S3 = S2 )
% 0.25/0.49 => ( member694524327on_trm @ ( produc1500300866on_trm @ R3 @ S3 ) @ R ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % ssubst_Pair_rhs
% 0.25/0.49 thf(fact_241_ssubst__Pair__rhs,axiom,
% 0.25/0.49 ! [R3: set_variable,S2: trm,R: set_Pr1235432374le_trm,S3: trm] :
% 0.25/0.49 ( ( member2122665623le_trm @ ( produc1482344242le_trm @ R3 @ S2 ) @ R )
% 0.25/0.49 => ( ( S3 = S2 )
% 0.25/0.49 => ( member2122665623le_trm @ ( produc1482344242le_trm @ R3 @ S3 ) @ R ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % ssubst_Pair_rhs
% 0.25/0.49 thf(fact_242_pred__equals__eq2,axiom,
% 0.25/0.49 ! [R: set_Pr622314946on_fml,S: set_Pr622314946on_fml] :
% 0.25/0.49 ( ( ( ^ [X3: option_game,Y3: option_fml] : ( member1883102883on_fml @ ( produc2124676926on_fml @ X3 @ Y3 ) @ R ) )
% 0.25/0.49 = ( ^ [X3: option_game,Y3: option_fml] : ( member1883102883on_fml @ ( produc2124676926on_fml @ X3 @ Y3 ) @ S ) ) )
% 0.25/0.49 = ( R = S ) ) ).
% 0.25/0.49
% 0.25/0.49 % pred_equals_eq2
% 0.25/0.49 thf(fact_243_pred__equals__eq2,axiom,
% 0.25/0.49 ! [R: set_Pr1471344007on_trm,S: set_Pr1471344007on_trm] :
% 0.25/0.49 ( ( ( ^ [X3: option_trm,Y3: option_trm] : ( member165817296on_trm @ ( produc709594775on_trm @ X3 @ Y3 ) @ R ) )
% 0.25/0.49 = ( ^ [X3: option_trm,Y3: option_trm] : ( member165817296on_trm @ ( produc709594775on_trm @ X3 @ Y3 ) @ S ) ) )
% 0.25/0.49 = ( R = S ) ) ).
% 0.25/0.49
% 0.25/0.49 % pred_equals_eq2
% 0.25/0.49 thf(fact_244_pred__equals__eq2,axiom,
% 0.25/0.49 ! [R: set_Pr927595527on_fml,S: set_Pr927595527on_fml] :
% 0.25/0.49 ( ( ( ^ [X3: option_fml,Y3: option_fml] : ( member1287158352on_fml @ ( produc909629463on_fml @ X3 @ Y3 ) @ R ) )
% 0.25/0.49 = ( ^ [X3: option_fml,Y3: option_fml] : ( member1287158352on_fml @ ( produc909629463on_fml @ X3 @ Y3 ) @ S ) ) )
% 0.25/0.49 = ( R = S ) ) ).
% 0.25/0.49
% 0.25/0.49 % pred_equals_eq2
% 0.25/0.49 thf(fact_245_pred__equals__eq2,axiom,
% 0.25/0.49 ! [R: set_Pr943832262on_trm,S: set_Pr943832262on_trm] :
% 0.25/0.49 ( ( ( ^ [X3: char,Y3: option_trm] : ( member694524327on_trm @ ( produc1500300866on_trm @ X3 @ Y3 ) @ R ) )
% 0.25/0.49 = ( ^ [X3: char,Y3: option_trm] : ( member694524327on_trm @ ( produc1500300866on_trm @ X3 @ Y3 ) @ S ) ) )
% 0.25/0.49 = ( R = S ) ) ).
% 0.25/0.49
% 0.25/0.49 % pred_equals_eq2
% 0.25/0.49 thf(fact_246_pred__equals__eq2,axiom,
% 0.25/0.49 ! [R: set_Pr1235432374le_trm,S: set_Pr1235432374le_trm] :
% 0.25/0.49 ( ( ( ^ [X3: set_variable,Y3: trm] : ( member2122665623le_trm @ ( produc1482344242le_trm @ X3 @ Y3 ) @ R ) )
% 0.25/0.49 = ( ^ [X3: set_variable,Y3: trm] : ( member2122665623le_trm @ ( produc1482344242le_trm @ X3 @ Y3 ) @ S ) ) )
% 0.25/0.49 = ( R = S ) ) ).
% 0.25/0.49
% 0.25/0.49 % pred_equals_eq2
% 0.25/0.49 thf(fact_247_pred__subset__eq2,axiom,
% 0.25/0.49 ! [R: set_Pr622314946on_fml,S: set_Pr622314946on_fml] :
% 0.25/0.49 ( ( ord_le1588489637_fml_o
% 0.25/0.49 @ ^ [X3: option_game,Y3: option_fml] : ( member1883102883on_fml @ ( produc2124676926on_fml @ X3 @ Y3 ) @ R )
% 0.25/0.49 @ ^ [X3: option_game,Y3: option_fml] : ( member1883102883on_fml @ ( produc2124676926on_fml @ X3 @ Y3 ) @ S ) )
% 0.25/0.49 = ( ord_le782333474on_fml @ R @ S ) ) ).
% 0.25/0.49
% 0.25/0.49 % pred_subset_eq2
% 0.25/0.49 thf(fact_248_pred__subset__eq2,axiom,
% 0.25/0.49 ! [R: set_Pr1471344007on_trm,S: set_Pr1471344007on_trm] :
% 0.25/0.49 ( ( ord_le847028878_trm_o
% 0.25/0.49 @ ^ [X3: option_trm,Y3: option_trm] : ( member165817296on_trm @ ( produc709594775on_trm @ X3 @ Y3 ) @ R )
% 0.25/0.49 @ ^ [X3: option_trm,Y3: option_trm] : ( member165817296on_trm @ ( produc709594775on_trm @ X3 @ Y3 ) @ S ) )
% 0.25/0.49 = ( ord_le1322722599on_trm @ R @ S ) ) ).
% 0.25/0.49
% 0.25/0.49 % pred_subset_eq2
% 0.25/0.49 thf(fact_249_pred__subset__eq2,axiom,
% 0.25/0.49 ! [R: set_Pr927595527on_fml,S: set_Pr927595527on_fml] :
% 0.25/0.49 ( ( ord_le802833166_fml_o
% 0.25/0.49 @ ^ [X3: option_fml,Y3: option_fml] : ( member1287158352on_fml @ ( produc909629463on_fml @ X3 @ Y3 ) @ R )
% 0.25/0.49 @ ^ [X3: option_fml,Y3: option_fml] : ( member1287158352on_fml @ ( produc909629463on_fml @ X3 @ Y3 ) @ S ) )
% 0.25/0.49 = ( ord_le778974119on_fml @ R @ S ) ) ).
% 0.25/0.49
% 0.25/0.49 % pred_subset_eq2
% 0.25/0.49 thf(fact_250_pred__subset__eq2,axiom,
% 0.25/0.49 ! [R: set_Pr943832262on_trm,S: set_Pr943832262on_trm] :
% 0.25/0.49 ( ( ord_le1890124833_trm_o
% 0.25/0.49 @ ^ [X3: char,Y3: option_trm] : ( member694524327on_trm @ ( produc1500300866on_trm @ X3 @ Y3 ) @ R )
% 0.25/0.49 @ ^ [X3: char,Y3: option_trm] : ( member694524327on_trm @ ( produc1500300866on_trm @ X3 @ Y3 ) @ S ) )
% 0.25/0.49 = ( ord_le541293862on_trm @ R @ S ) ) ).
% 0.25/0.49
% 0.25/0.49 % pred_subset_eq2
% 0.25/0.49 thf(fact_251_pred__subset__eq2,axiom,
% 0.25/0.49 ! [R: set_Pr1235432374le_trm,S: set_Pr1235432374le_trm] :
% 0.25/0.49 ( ( ord_le691957041_trm_o
% 0.25/0.49 @ ^ [X3: set_variable,Y3: trm] : ( member2122665623le_trm @ ( produc1482344242le_trm @ X3 @ Y3 ) @ R )
% 0.25/0.49 @ ^ [X3: set_variable,Y3: trm] : ( member2122665623le_trm @ ( produc1482344242le_trm @ X3 @ Y3 ) @ S ) )
% 0.25/0.49 = ( ord_le2102862870le_trm @ R @ S ) ) ).
% 0.25/0.49
% 0.25/0.49 % pred_subset_eq2
% 0.25/0.49 thf(fact_252_option_Odisc__eq__case_I1_J,axiom,
% 0.25/0.49 ! [Option: option_trm] :
% 0.25/0.49 ( ( Option = none_trm )
% 0.25/0.49 = ( case_option_o_trm @ $true
% 0.25/0.49 @ ^ [Uu: trm] : $false
% 0.25/0.49 @ Option ) ) ).
% 0.25/0.49
% 0.25/0.49 % option.disc_eq_case(1)
% 0.25/0.49 thf(fact_253_option_Odisc__eq__case_I1_J,axiom,
% 0.25/0.49 ! [Option: option_fml] :
% 0.25/0.49 ( ( Option = none_fml )
% 0.25/0.49 = ( case_option_o_fml @ $true
% 0.25/0.49 @ ^ [Uu: fml] : $false
% 0.25/0.49 @ Option ) ) ).
% 0.25/0.49
% 0.25/0.49 % option.disc_eq_case(1)
% 0.25/0.49 thf(fact_254_option_Odisc__eq__case_I1_J,axiom,
% 0.25/0.49 ! [Option: option_game] :
% 0.25/0.49 ( ( Option = none_game )
% 0.25/0.49 = ( case_option_o_game @ $true
% 0.25/0.49 @ ^ [Uu: game] : $false
% 0.25/0.49 @ Option ) ) ).
% 0.25/0.49
% 0.25/0.49 % option.disc_eq_case(1)
% 0.25/0.49 thf(fact_255_option_Odisc__eq__case_I2_J,axiom,
% 0.25/0.49 ! [Option: option_trm] :
% 0.25/0.49 ( ( Option != none_trm )
% 0.25/0.49 = ( case_option_o_trm @ $false
% 0.25/0.49 @ ^ [Uu: trm] : $true
% 0.25/0.49 @ Option ) ) ).
% 0.25/0.49
% 0.25/0.49 % option.disc_eq_case(2)
% 0.25/0.49 thf(fact_256_option_Odisc__eq__case_I2_J,axiom,
% 0.25/0.49 ! [Option: option_fml] :
% 0.25/0.49 ( ( Option != none_fml )
% 0.25/0.49 = ( case_option_o_fml @ $false
% 0.25/0.49 @ ^ [Uu: fml] : $true
% 0.25/0.49 @ Option ) ) ).
% 0.25/0.49
% 0.25/0.49 % option.disc_eq_case(2)
% 0.25/0.49 thf(fact_257_option_Odisc__eq__case_I2_J,axiom,
% 0.25/0.49 ! [Option: option_game] :
% 0.25/0.49 ( ( Option != none_game )
% 0.25/0.49 = ( case_option_o_game @ $false
% 0.25/0.49 @ ^ [Uu: game] : $true
% 0.25/0.49 @ Option ) ) ).
% 0.25/0.49
% 0.25/0.49 % option.disc_eq_case(2)
% 0.25/0.49 thf(fact_258_Timeso_Ocases,axiom,
% 0.25/0.49 ! [X2: produc1072747943on_trm] :
% 0.25/0.49 ( ! [Theta2: trm,Eta2: trm] :
% 0.25/0.49 ( X2
% 0.25/0.49 != ( produc709594775on_trm @ ( some_trm @ Theta2 ) @ ( some_trm @ Eta2 ) ) )
% 0.25/0.49 => ( ! [Eta2: option_trm] :
% 0.25/0.49 ( X2
% 0.25/0.49 != ( produc709594775on_trm @ none_trm @ Eta2 ) )
% 0.25/0.49 => ~ ! [V2: trm] :
% 0.25/0.49 ( X2
% 0.25/0.49 != ( produc709594775on_trm @ ( some_trm @ V2 ) @ none_trm ) ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % Timeso.cases
% 0.25/0.49 thf(fact_259_case__optionE,axiom,
% 0.25/0.49 ! [P: $o,Q: trm > $o,X2: option_trm] :
% 0.25/0.49 ( ( case_option_o_trm @ P @ Q @ X2 )
% 0.25/0.49 => ( ( ( X2 = none_trm )
% 0.25/0.49 => ~ P )
% 0.25/0.49 => ~ ! [Y4: trm] :
% 0.25/0.49 ( ( X2
% 0.25/0.49 = ( some_trm @ Y4 ) )
% 0.25/0.49 => ~ ( Q @ Y4 ) ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % case_optionE
% 0.25/0.49 thf(fact_260_case__optionE,axiom,
% 0.25/0.49 ! [P: $o,Q: fml > $o,X2: option_fml] :
% 0.25/0.49 ( ( case_option_o_fml @ P @ Q @ X2 )
% 0.25/0.49 => ( ( ( X2 = none_fml )
% 0.25/0.49 => ~ P )
% 0.25/0.49 => ~ ! [Y4: fml] :
% 0.25/0.49 ( ( X2
% 0.25/0.49 = ( some_fml @ Y4 ) )
% 0.25/0.49 => ~ ( Q @ Y4 ) ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % case_optionE
% 0.25/0.49 thf(fact_261_case__optionE,axiom,
% 0.25/0.49 ! [P: $o,Q: game > $o,X2: option_game] :
% 0.25/0.49 ( ( case_option_o_game @ P @ Q @ X2 )
% 0.25/0.49 => ( ( ( X2 = none_game )
% 0.25/0.49 => ~ P )
% 0.25/0.49 => ~ ! [Y4: game] :
% 0.25/0.49 ( ( X2
% 0.25/0.49 = ( some_game @ Y4 ) )
% 0.25/0.49 => ~ ( Q @ Y4 ) ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % case_optionE
% 0.25/0.49 thf(fact_262_Timeso_Opelims,axiom,
% 0.25/0.49 ! [X2: option_trm,Xa: option_trm,Y2: option_trm] :
% 0.25/0.49 ( ( ( uSubst918876924Timeso @ X2 @ Xa )
% 0.25/0.49 = Y2 )
% 0.25/0.49 => ( ( accp_P758790320on_trm @ uSubst924844285so_rel @ ( produc709594775on_trm @ X2 @ Xa ) )
% 0.25/0.49 => ( ! [Theta2: trm] :
% 0.25/0.49 ( ( X2
% 0.25/0.49 = ( some_trm @ Theta2 ) )
% 0.25/0.49 => ! [Eta2: trm] :
% 0.25/0.49 ( ( Xa
% 0.25/0.49 = ( some_trm @ Eta2 ) )
% 0.25/0.49 => ( ( Y2
% 0.25/0.49 = ( some_trm @ ( times @ Theta2 @ Eta2 ) ) )
% 0.25/0.49 => ~ ( accp_P758790320on_trm @ uSubst924844285so_rel @ ( produc709594775on_trm @ ( some_trm @ Theta2 ) @ ( some_trm @ Eta2 ) ) ) ) ) )
% 0.25/0.49 => ( ( ( X2 = none_trm )
% 0.25/0.49 => ( ( Y2 = none_trm )
% 0.25/0.49 => ~ ( accp_P758790320on_trm @ uSubst924844285so_rel @ ( produc709594775on_trm @ none_trm @ Xa ) ) ) )
% 0.25/0.49 => ~ ! [V2: trm] :
% 0.25/0.49 ( ( X2
% 0.25/0.49 = ( some_trm @ V2 ) )
% 0.25/0.49 => ( ( Xa = none_trm )
% 0.25/0.49 => ( ( Y2 = none_trm )
% 0.25/0.49 => ~ ( accp_P758790320on_trm @ uSubst924844285so_rel @ ( produc709594775on_trm @ ( some_trm @ V2 ) @ none_trm ) ) ) ) ) ) ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % Timeso.pelims
% 0.25/0.49 thf(fact_263_Pluso_Opelims,axiom,
% 0.25/0.49 ! [X2: option_trm,Xa: option_trm,Y2: option_trm] :
% 0.25/0.49 ( ( ( uSubst141955042_Pluso @ X2 @ Xa )
% 0.25/0.49 = Y2 )
% 0.25/0.49 => ( ( accp_P758790320on_trm @ uSubst691094423so_rel @ ( produc709594775on_trm @ X2 @ Xa ) )
% 0.25/0.49 => ( ! [Theta2: trm] :
% 0.25/0.49 ( ( X2
% 0.25/0.49 = ( some_trm @ Theta2 ) )
% 0.25/0.49 => ! [Eta2: trm] :
% 0.25/0.49 ( ( Xa
% 0.25/0.49 = ( some_trm @ Eta2 ) )
% 0.25/0.49 => ( ( Y2
% 0.25/0.49 = ( some_trm @ ( plus @ Theta2 @ Eta2 ) ) )
% 0.25/0.49 => ~ ( accp_P758790320on_trm @ uSubst691094423so_rel @ ( produc709594775on_trm @ ( some_trm @ Theta2 ) @ ( some_trm @ Eta2 ) ) ) ) ) )
% 0.25/0.49 => ( ( ( X2 = none_trm )
% 0.25/0.49 => ( ( Y2 = none_trm )
% 0.25/0.49 => ~ ( accp_P758790320on_trm @ uSubst691094423so_rel @ ( produc709594775on_trm @ none_trm @ Xa ) ) ) )
% 0.25/0.49 => ~ ! [V2: trm] :
% 0.25/0.49 ( ( X2
% 0.25/0.49 = ( some_trm @ V2 ) )
% 0.25/0.49 => ( ( Xa = none_trm )
% 0.25/0.49 => ( ( Y2 = none_trm )
% 0.25/0.49 => ~ ( accp_P758790320on_trm @ uSubst691094423so_rel @ ( produc709594775on_trm @ ( some_trm @ V2 ) @ none_trm ) ) ) ) ) ) ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % Pluso.pelims
% 0.25/0.49 thf(fact_264_ODEo_Ocases,axiom,
% 0.25/0.49 ! [X2: produc464795408on_trm] :
% 0.25/0.49 ( ! [X: char,Theta2: trm] :
% 0.25/0.49 ( X2
% 0.25/0.49 != ( produc1500300866on_trm @ X @ ( some_trm @ Theta2 ) ) )
% 0.25/0.49 => ~ ! [X: char] :
% 0.25/0.49 ( X2
% 0.25/0.49 != ( produc1500300866on_trm @ X @ none_trm ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % ODEo.cases
% 0.25/0.49 thf(fact_265_Assigno_Ocases,axiom,
% 0.25/0.49 ! [X2: produc1024976764on_trm] :
% 0.25/0.49 ( ! [X: variable,Theta2: trm] :
% 0.25/0.49 ( X2
% 0.25/0.49 != ( produc1743721902on_trm @ X @ ( some_trm @ Theta2 ) ) )
% 0.25/0.49 => ~ ! [X: variable] :
% 0.25/0.49 ( X2
% 0.25/0.49 != ( produc1743721902on_trm @ X @ none_trm ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % Assigno.cases
% 0.25/0.49 thf(fact_266_Composeo_Ocases,axiom,
% 0.25/0.49 ! [X2: produc1016592119n_game] :
% 0.25/0.49 ( ! [Alpha: game,Beta: game] :
% 0.25/0.49 ( X2
% 0.25/0.49 != ( produc1111617711n_game @ ( some_game @ Alpha ) @ ( some_game @ Beta ) ) )
% 0.25/0.49 => ( ! [Alpha: option_game] :
% 0.25/0.49 ( X2
% 0.25/0.49 != ( produc1111617711n_game @ Alpha @ none_game ) )
% 0.25/0.49 => ~ ! [V2: game] :
% 0.25/0.49 ( X2
% 0.25/0.49 != ( produc1111617711n_game @ none_game @ ( some_game @ V2 ) ) ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % Composeo.cases
% 0.25/0.49 thf(fact_267_Existso_Ocases,axiom,
% 0.25/0.49 ! [X2: produc1408538418on_fml] :
% 0.25/0.49 ( ! [X: variable,Phi2: fml] :
% 0.25/0.49 ( X2
% 0.25/0.49 != ( produc1205977188on_fml @ X @ ( some_fml @ Phi2 ) ) )
% 0.25/0.49 => ~ ! [X: variable] :
% 0.25/0.49 ( X2
% 0.25/0.49 != ( produc1205977188on_fml @ X @ none_fml ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % Existso.cases
% 0.25/0.49 thf(fact_268_Ando_Ocases,axiom,
% 0.25/0.49 ! [X2: produc46605351on_fml] :
% 0.25/0.49 ( ! [Phi2: fml,Psi: fml] :
% 0.25/0.49 ( X2
% 0.25/0.49 != ( produc909629463on_fml @ ( some_fml @ Phi2 ) @ ( some_fml @ Psi ) ) )
% 0.25/0.49 => ( ! [Psi: option_fml] :
% 0.25/0.49 ( X2
% 0.25/0.49 != ( produc909629463on_fml @ none_fml @ Psi ) )
% 0.25/0.49 => ~ ! [V2: fml] :
% 0.25/0.49 ( X2
% 0.25/0.49 != ( produc909629463on_fml @ ( some_fml @ V2 ) @ none_fml ) ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % Ando.cases
% 0.25/0.49 thf(fact_269_usubstappt_Opsimps_I7_J,axiom,
% 0.25/0.49 ! [Sigma: produc1418842292n_game,U: set_variable,Theta: trm] :
% 0.25/0.49 ( ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ Sigma @ ( produc1482344242le_trm @ U @ ( differential @ Theta ) ) ) )
% 0.25/0.49 => ( ( uSubst516392818stappt @ Sigma @ U @ ( differential @ Theta ) )
% 0.25/0.49 = ( uSubst716837505ntialo
% 0.25/0.49 @ ( uSubst516392818stappt @ Sigma
% 0.25/0.49 @ ( collect_variable
% 0.25/0.49 @ ^ [X3: variable] : $true )
% 0.25/0.49 @ Theta ) ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % usubstappt.psimps(7)
% 0.25/0.49 thf(fact_270_usubstappt_Opsimps_I6_J,axiom,
% 0.25/0.49 ! [Sigma: produc1418842292n_game,U: set_variable,Theta: trm,Eta: trm] :
% 0.25/0.49 ( ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ Sigma @ ( produc1482344242le_trm @ U @ ( times @ Theta @ Eta ) ) ) )
% 0.25/0.49 => ( ( uSubst516392818stappt @ Sigma @ U @ ( times @ Theta @ Eta ) )
% 0.25/0.49 = ( uSubst918876924Timeso @ ( uSubst516392818stappt @ Sigma @ U @ Theta ) @ ( uSubst516392818stappt @ Sigma @ U @ Eta ) ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % usubstappt.psimps(6)
% 0.25/0.49 thf(fact_271_usubstappt_Opsimps_I5_J,axiom,
% 0.25/0.49 ! [Sigma: produc1418842292n_game,U: set_variable,Theta: trm,Eta: trm] :
% 0.25/0.49 ( ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ Sigma @ ( produc1482344242le_trm @ U @ ( plus @ Theta @ Eta ) ) ) )
% 0.25/0.49 => ( ( uSubst516392818stappt @ Sigma @ U @ ( plus @ Theta @ Eta ) )
% 0.25/0.49 = ( uSubst141955042_Pluso @ ( uSubst516392818stappt @ Sigma @ U @ Theta ) @ ( uSubst516392818stappt @ Sigma @ U @ Eta ) ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % usubstappt.psimps(5)
% 0.25/0.49 thf(fact_272_usubstappt_Opsimps_I1_J,axiom,
% 0.25/0.49 ! [Sigma: produc1418842292n_game,U: set_variable,X2: variable] :
% 0.25/0.49 ( ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ Sigma @ ( produc1482344242le_trm @ U @ ( var @ X2 ) ) ) )
% 0.25/0.49 => ( ( uSubst516392818stappt @ Sigma @ U @ ( var @ X2 ) )
% 0.25/0.49 = ( some_trm @ ( var @ X2 ) ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % usubstappt.psimps(1)
% 0.25/0.49 thf(fact_273_usubstappt_Opsimps_I2_J,axiom,
% 0.25/0.49 ! [Sigma: produc1418842292n_game,U: set_variable,R3: real] :
% 0.25/0.49 ( ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ Sigma @ ( produc1482344242le_trm @ U @ ( number @ R3 ) ) ) )
% 0.25/0.49 => ( ( uSubst516392818stappt @ Sigma @ U @ ( number @ R3 ) )
% 0.25/0.49 = ( some_trm @ ( number @ R3 ) ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % usubstappt.psimps(2)
% 0.25/0.49 thf(fact_274_in__lex__prod,axiom,
% 0.25/0.49 ! [A3: option_trm,B3: option_fml,A6: option_trm,B6: option_fml,R3: set_Pr1471344007on_trm,S2: set_Pr927595527on_fml] :
% 0.25/0.49 ( ( member1316917136on_fml @ ( produc1235825367on_fml @ ( produc171850061on_fml @ A3 @ B3 ) @ ( produc171850061on_fml @ A6 @ B6 ) ) @ ( lex_pr1724583269on_fml @ R3 @ S2 ) )
% 0.25/0.49 = ( ( member165817296on_trm @ ( produc709594775on_trm @ A3 @ A6 ) @ R3 )
% 0.25/0.49 | ( ( A3 = A6 )
% 0.25/0.49 & ( member1287158352on_fml @ ( produc909629463on_fml @ B3 @ B6 ) @ S2 ) ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % in_lex_prod
% 0.25/0.49 thf(fact_275_in__lex__prod,axiom,
% 0.25/0.49 ! [A3: option_fml,B3: option_trm,A6: option_fml,B6: option_trm,R3: set_Pr927595527on_fml,S2: set_Pr1471344007on_trm] :
% 0.25/0.49 ( ( member1883874960on_trm @ ( produc2132972503on_trm @ ( produc1447374177on_trm @ A3 @ B3 ) @ ( produc1447374177on_trm @ A6 @ B6 ) ) @ ( lex_pr852623737on_trm @ R3 @ S2 ) )
% 0.25/0.49 = ( ( member1287158352on_fml @ ( produc909629463on_fml @ A3 @ A6 ) @ R3 )
% 0.25/0.49 | ( ( A3 = A6 )
% 0.25/0.49 & ( member165817296on_trm @ ( produc709594775on_trm @ B3 @ B6 ) @ S2 ) ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % in_lex_prod
% 0.25/0.49 thf(fact_276_in__lex__prod,axiom,
% 0.25/0.49 ! [A3: option_game,B3: option_fml,A6: option_game,B6: option_fml,R3: set_Pr1625152599n_game,S2: set_Pr927595527on_fml] :
% 0.25/0.49 ( ( member113767842on_fml @ ( produc556056113on_fml @ ( produc2124676926on_fml @ A3 @ B3 ) @ ( produc2124676926on_fml @ A6 @ B6 ) ) @ ( lex_pr425996582on_fml @ R3 @ S2 ) )
% 0.25/0.49 = ( ( member191809696n_game @ ( produc1111617711n_game @ A3 @ A6 ) @ R3 )
% 0.25/0.49 | ( ( A3 = A6 )
% 0.25/0.49 & ( member1287158352on_fml @ ( produc909629463on_fml @ B3 @ B6 ) @ S2 ) ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % in_lex_prod
% 0.25/0.49 thf(fact_277_in__lex__prod,axiom,
% 0.25/0.49 ! [A3: option_trm,B3: option_trm,A6: option_trm,B6: option_trm,R3: set_Pr1471344007on_trm,S2: set_Pr1471344007on_trm] :
% 0.25/0.49 ( ( member602811152on_trm @ ( produc2001752919on_trm @ ( produc709594775on_trm @ A3 @ B3 ) @ ( produc709594775on_trm @ A6 @ B6 ) ) @ ( lex_pr114844335on_trm @ R3 @ S2 ) )
% 0.25/0.49 = ( ( member165817296on_trm @ ( produc709594775on_trm @ A3 @ A6 ) @ R3 )
% 0.25/0.49 | ( ( A3 = A6 )
% 0.25/0.49 & ( member165817296on_trm @ ( produc709594775on_trm @ B3 @ B6 ) @ S2 ) ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % in_lex_prod
% 0.25/0.49 thf(fact_278_in__lex__prod,axiom,
% 0.25/0.49 ! [A3: option_fml,B3: option_fml,A6: option_fml,B6: option_fml,R3: set_Pr927595527on_fml,S2: set_Pr927595527on_fml] :
% 0.25/0.49 ( ( member450497296on_fml @ ( produc1367044951on_fml @ ( produc909629463on_fml @ A3 @ B3 ) @ ( produc909629463on_fml @ A6 @ B6 ) ) @ ( lex_pr314879023on_fml @ R3 @ S2 ) )
% 0.25/0.49 = ( ( member1287158352on_fml @ ( produc909629463on_fml @ A3 @ A6 ) @ R3 )
% 0.25/0.49 | ( ( A3 = A6 )
% 0.25/0.49 & ( member1287158352on_fml @ ( produc909629463on_fml @ B3 @ B6 ) @ S2 ) ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % in_lex_prod
% 0.25/0.49 thf(fact_279_in__lex__prod,axiom,
% 0.25/0.49 ! [A3: char,B3: option_trm,A6: char,B6: option_trm,R3: set_Pr604539619r_char,S2: set_Pr1471344007on_trm] :
% 0.25/0.49 ( ( member1950256170on_trm @ ( produc444919481on_trm @ ( produc1500300866on_trm @ A3 @ B3 ) @ ( produc1500300866on_trm @ A6 @ B6 ) ) @ ( lex_pr1901327402on_trm @ R3 @ S2 ) )
% 0.25/0.49 = ( ( member1866856748r_char @ ( produc19545147r_char @ A3 @ A6 ) @ R3 )
% 0.25/0.49 | ( ( A3 = A6 )
% 0.25/0.49 & ( member165817296on_trm @ ( produc709594775on_trm @ B3 @ B6 ) @ S2 ) ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % in_lex_prod
% 0.25/0.49 thf(fact_280_in__lex__prod,axiom,
% 0.25/0.49 ! [A3: set_variable,B3: trm,A6: set_variable,B6: trm,R3: set_Pr181266295riable,S2: set_Pr491793543rm_trm] :
% 0.25/0.49 ( ( member1150310282le_trm @ ( produc1056455193le_trm @ ( produc1482344242le_trm @ A3 @ B3 ) @ ( produc1482344242le_trm @ A6 @ B6 ) ) @ ( lex_pr1522821402le_trm @ R3 @ S2 ) )
% 0.25/0.49 = ( ( member1978718144riable @ ( produc1766592463riable @ A3 @ A6 ) @ R3 )
% 0.25/0.49 | ( ( A3 = A6 )
% 0.25/0.49 & ( member1735386832rm_trm @ ( product_Pair_trm_trm @ B3 @ B6 ) @ S2 ) ) ) ) ).
% 0.25/0.49
% 0.25/0.49 % in_lex_prod
% 0.25/0.49 thf(fact_281_trm_Oinject_I2_J,axiom,
% 0.25/0.49 ! [X23: real,Y23: real] :
% 0.25/0.49 ( ( ( number @ X23 )
% 0.25/0.50 = ( number @ Y23 ) )
% 0.25/0.50 = ( X23 = Y23 ) ) ).
% 0.25/0.50
% 0.25/0.50 % trm.inject(2)
% 0.25/0.50 thf(fact_282_trm_Oinject_I1_J,axiom,
% 0.25/0.50 ! [X1: variable,Y1: variable] :
% 0.25/0.50 ( ( ( var @ X1 )
% 0.25/0.50 = ( var @ Y1 ) )
% 0.25/0.50 = ( X1 = Y1 ) ) ).
% 0.25/0.50
% 0.25/0.50 % trm.inject(1)
% 0.25/0.50 thf(fact_283_trm_Odistinct_I17_J,axiom,
% 0.25/0.50 ! [X23: real,X51: trm,X52: trm] :
% 0.25/0.50 ( ( number @ X23 )
% 0.25/0.50 != ( plus @ X51 @ X52 ) ) ).
% 0.25/0.50
% 0.25/0.50 % trm.distinct(17)
% 0.25/0.50 thf(fact_284_trm_Odistinct_I19_J,axiom,
% 0.25/0.50 ! [X23: real,X61: trm,X62: trm] :
% 0.25/0.50 ( ( number @ X23 )
% 0.25/0.50 != ( times @ X61 @ X62 ) ) ).
% 0.25/0.50
% 0.25/0.50 % trm.distinct(19)
% 0.25/0.50 thf(fact_285_trm_Odistinct_I21_J,axiom,
% 0.25/0.50 ! [X23: real,X7: trm] :
% 0.25/0.50 ( ( number @ X23 )
% 0.25/0.50 != ( differential @ X7 ) ) ).
% 0.25/0.50
% 0.25/0.50 % trm.distinct(21)
% 0.25/0.50 thf(fact_286_trm_Odistinct_I7_J,axiom,
% 0.25/0.50 ! [X1: variable,X51: trm,X52: trm] :
% 0.25/0.50 ( ( var @ X1 )
% 0.25/0.50 != ( plus @ X51 @ X52 ) ) ).
% 0.25/0.50
% 0.25/0.50 % trm.distinct(7)
% 0.25/0.50 thf(fact_287_trm_Odistinct_I9_J,axiom,
% 0.25/0.50 ! [X1: variable,X61: trm,X62: trm] :
% 0.25/0.50 ( ( var @ X1 )
% 0.25/0.50 != ( times @ X61 @ X62 ) ) ).
% 0.25/0.50
% 0.25/0.50 % trm.distinct(9)
% 0.25/0.50 thf(fact_288_trm_Odistinct_I11_J,axiom,
% 0.25/0.50 ! [X1: variable,X7: trm] :
% 0.25/0.50 ( ( var @ X1 )
% 0.25/0.50 != ( differential @ X7 ) ) ).
% 0.25/0.50
% 0.25/0.50 % trm.distinct(11)
% 0.25/0.50 thf(fact_289_trm_Odistinct_I1_J,axiom,
% 0.25/0.50 ! [X1: variable,X23: real] :
% 0.25/0.50 ( ( var @ X1 )
% 0.25/0.50 != ( number @ X23 ) ) ).
% 0.25/0.50
% 0.25/0.50 % trm.distinct(1)
% 0.25/0.50 thf(fact_290_usubstappt_Osimps_I2_J,axiom,
% 0.25/0.50 ! [Sigma: produc1418842292n_game,U: set_variable,R3: real] :
% 0.25/0.50 ( ( uSubst516392818stappt @ Sigma @ U @ ( number @ R3 ) )
% 0.25/0.50 = ( some_trm @ ( number @ R3 ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % usubstappt.simps(2)
% 0.25/0.50 thf(fact_291_usubstappt_Osimps_I1_J,axiom,
% 0.25/0.50 ! [Sigma: produc1418842292n_game,U: set_variable,X2: variable] :
% 0.25/0.50 ( ( uSubst516392818stappt @ Sigma @ U @ ( var @ X2 ) )
% 0.25/0.50 = ( some_trm @ ( var @ X2 ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % usubstappt.simps(1)
% 0.25/0.50 thf(fact_292_usubstappt_Ocases,axiom,
% 0.25/0.50 ! [X2: produc1699626005le_trm] :
% 0.25/0.50 ( ! [Sigma2: produc1418842292n_game,U3: set_variable,X: variable] :
% 0.25/0.50 ( X2
% 0.25/0.50 != ( produc2015636557le_trm @ Sigma2 @ ( produc1482344242le_trm @ U3 @ ( var @ X ) ) ) )
% 0.25/0.50 => ( ! [Sigma2: produc1418842292n_game,U3: set_variable,R5: real] :
% 0.25/0.50 ( X2
% 0.25/0.50 != ( produc2015636557le_trm @ Sigma2 @ ( produc1482344242le_trm @ U3 @ ( number @ R5 ) ) ) )
% 0.25/0.50 => ( ! [Sigma2: produc1418842292n_game,U3: set_variable,F3: char] :
% 0.25/0.50 ( X2
% 0.25/0.50 != ( produc2015636557le_trm @ Sigma2 @ ( produc1482344242le_trm @ U3 @ ( const @ F3 ) ) ) )
% 0.25/0.50 => ( ! [Sigma2: produc1418842292n_game,U3: set_variable,F3: char,Theta2: trm] :
% 0.25/0.50 ( X2
% 0.25/0.50 != ( produc2015636557le_trm @ Sigma2 @ ( produc1482344242le_trm @ U3 @ ( func @ F3 @ Theta2 ) ) ) )
% 0.25/0.50 => ( ! [Sigma2: produc1418842292n_game,U3: set_variable,Theta2: trm,Eta2: trm] :
% 0.25/0.50 ( X2
% 0.25/0.50 != ( produc2015636557le_trm @ Sigma2 @ ( produc1482344242le_trm @ U3 @ ( plus @ Theta2 @ Eta2 ) ) ) )
% 0.25/0.50 => ( ! [Sigma2: produc1418842292n_game,U3: set_variable,Theta2: trm,Eta2: trm] :
% 0.25/0.50 ( X2
% 0.25/0.50 != ( produc2015636557le_trm @ Sigma2 @ ( produc1482344242le_trm @ U3 @ ( times @ Theta2 @ Eta2 ) ) ) )
% 0.25/0.50 => ~ ! [Sigma2: produc1418842292n_game,U3: set_variable,Theta2: trm] :
% 0.25/0.50 ( X2
% 0.25/0.50 != ( produc2015636557le_trm @ Sigma2 @ ( produc1482344242le_trm @ U3 @ ( differential @ Theta2 ) ) ) ) ) ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % usubstappt.cases
% 0.25/0.50 thf(fact_293_Testo_Osimps_I2_J,axiom,
% 0.25/0.50 ( ( uSubst1367128042_Testo @ none_fml )
% 0.25/0.50 = none_game ) ).
% 0.25/0.50
% 0.25/0.50 % Testo.simps(2)
% 0.25/0.50 thf(fact_294_Testo__undef,axiom,
% 0.25/0.50 ! [Phi: option_fml] :
% 0.25/0.50 ( ( ( uSubst1367128042_Testo @ Phi )
% 0.25/0.50 = none_game )
% 0.25/0.50 = ( Phi = none_fml ) ) ).
% 0.25/0.50
% 0.25/0.50 % Testo_undef
% 0.25/0.50 thf(fact_295_trm_Oinject_I4_J,axiom,
% 0.25/0.50 ! [X41: char,X42: trm,Y41: char,Y42: trm] :
% 0.25/0.50 ( ( ( func @ X41 @ X42 )
% 0.25/0.50 = ( func @ Y41 @ Y42 ) )
% 0.25/0.50 = ( ( X41 = Y41 )
% 0.25/0.50 & ( X42 = Y42 ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % trm.inject(4)
% 0.25/0.50 thf(fact_296_trm_Oinject_I3_J,axiom,
% 0.25/0.50 ! [X32: char,Y32: char] :
% 0.25/0.50 ( ( ( const @ X32 )
% 0.25/0.50 = ( const @ Y32 ) )
% 0.25/0.50 = ( X32 = Y32 ) ) ).
% 0.25/0.50
% 0.25/0.50 % trm.inject(3)
% 0.25/0.50 thf(fact_297_trm_Odistinct_I3_J,axiom,
% 0.25/0.50 ! [X1: variable,X32: char] :
% 0.25/0.50 ( ( var @ X1 )
% 0.25/0.50 != ( const @ X32 ) ) ).
% 0.25/0.50
% 0.25/0.50 % trm.distinct(3)
% 0.25/0.50 thf(fact_298_trm_Odistinct_I5_J,axiom,
% 0.25/0.50 ! [X1: variable,X41: char,X42: trm] :
% 0.25/0.50 ( ( var @ X1 )
% 0.25/0.50 != ( func @ X41 @ X42 ) ) ).
% 0.25/0.50
% 0.25/0.50 % trm.distinct(5)
% 0.25/0.50 thf(fact_299_trm_Odistinct_I13_J,axiom,
% 0.25/0.50 ! [X23: real,X32: char] :
% 0.25/0.50 ( ( number @ X23 )
% 0.25/0.50 != ( const @ X32 ) ) ).
% 0.25/0.50
% 0.25/0.50 % trm.distinct(13)
% 0.25/0.50 thf(fact_300_trm_Odistinct_I15_J,axiom,
% 0.25/0.50 ! [X23: real,X41: char,X42: trm] :
% 0.25/0.50 ( ( number @ X23 )
% 0.25/0.50 != ( func @ X41 @ X42 ) ) ).
% 0.25/0.50
% 0.25/0.50 % trm.distinct(15)
% 0.25/0.50 thf(fact_301_trm_Odistinct_I23_J,axiom,
% 0.25/0.50 ! [X32: char,X41: char,X42: trm] :
% 0.25/0.50 ( ( const @ X32 )
% 0.25/0.50 != ( func @ X41 @ X42 ) ) ).
% 0.25/0.50
% 0.25/0.50 % trm.distinct(23)
% 0.25/0.50 thf(fact_302_trm_Odistinct_I29_J,axiom,
% 0.25/0.50 ! [X32: char,X7: trm] :
% 0.25/0.50 ( ( const @ X32 )
% 0.25/0.50 != ( differential @ X7 ) ) ).
% 0.25/0.50
% 0.25/0.50 % trm.distinct(29)
% 0.25/0.50 thf(fact_303_trm_Odistinct_I27_J,axiom,
% 0.25/0.50 ! [X32: char,X61: trm,X62: trm] :
% 0.25/0.50 ( ( const @ X32 )
% 0.25/0.50 != ( times @ X61 @ X62 ) ) ).
% 0.25/0.50
% 0.25/0.50 % trm.distinct(27)
% 0.25/0.50 thf(fact_304_trm_Odistinct_I25_J,axiom,
% 0.25/0.50 ! [X32: char,X51: trm,X52: trm] :
% 0.25/0.50 ( ( const @ X32 )
% 0.25/0.50 != ( plus @ X51 @ X52 ) ) ).
% 0.25/0.50
% 0.25/0.50 % trm.distinct(25)
% 0.25/0.50 thf(fact_305_trm_Odistinct_I35_J,axiom,
% 0.25/0.50 ! [X41: char,X42: trm,X7: trm] :
% 0.25/0.50 ( ( func @ X41 @ X42 )
% 0.25/0.50 != ( differential @ X7 ) ) ).
% 0.25/0.50
% 0.25/0.50 % trm.distinct(35)
% 0.25/0.50 thf(fact_306_trm_Odistinct_I33_J,axiom,
% 0.25/0.50 ! [X41: char,X42: trm,X61: trm,X62: trm] :
% 0.25/0.50 ( ( func @ X41 @ X42 )
% 0.25/0.50 != ( times @ X61 @ X62 ) ) ).
% 0.25/0.50
% 0.25/0.50 % trm.distinct(33)
% 0.25/0.50 thf(fact_307_trm_Odistinct_I31_J,axiom,
% 0.25/0.50 ! [X41: char,X42: trm,X51: trm,X52: trm] :
% 0.25/0.50 ( ( func @ X41 @ X42 )
% 0.25/0.50 != ( plus @ X51 @ X52 ) ) ).
% 0.25/0.50
% 0.25/0.50 % trm.distinct(31)
% 0.25/0.50 thf(fact_308_trm_Oinduct,axiom,
% 0.25/0.50 ! [P: trm > $o,Trm: trm] :
% 0.25/0.50 ( ! [X: variable] : ( P @ ( var @ X ) )
% 0.25/0.50 => ( ! [X: real] : ( P @ ( number @ X ) )
% 0.25/0.50 => ( ! [X: char] : ( P @ ( const @ X ) )
% 0.25/0.50 => ( ! [X1a: char,X2a: trm] :
% 0.25/0.50 ( ( P @ X2a )
% 0.25/0.50 => ( P @ ( func @ X1a @ X2a ) ) )
% 0.25/0.50 => ( ! [X1a: trm,X2a: trm] :
% 0.25/0.50 ( ( P @ X1a )
% 0.25/0.50 => ( ( P @ X2a )
% 0.25/0.50 => ( P @ ( plus @ X1a @ X2a ) ) ) )
% 0.25/0.50 => ( ! [X1a: trm,X2a: trm] :
% 0.25/0.50 ( ( P @ X1a )
% 0.25/0.50 => ( ( P @ X2a )
% 0.25/0.50 => ( P @ ( times @ X1a @ X2a ) ) ) )
% 0.25/0.50 => ( ! [X: trm] :
% 0.25/0.50 ( ( P @ X )
% 0.25/0.50 => ( P @ ( differential @ X ) ) )
% 0.25/0.50 => ( P @ Trm ) ) ) ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % trm.induct
% 0.25/0.50 thf(fact_309_trm_Oexhaust,axiom,
% 0.25/0.50 ! [Y2: trm] :
% 0.25/0.50 ( ! [X12: variable] :
% 0.25/0.50 ( Y2
% 0.25/0.50 != ( var @ X12 ) )
% 0.25/0.50 => ( ! [X24: real] :
% 0.25/0.50 ( Y2
% 0.25/0.50 != ( number @ X24 ) )
% 0.25/0.50 => ( ! [X33: char] :
% 0.25/0.50 ( Y2
% 0.25/0.50 != ( const @ X33 ) )
% 0.25/0.50 => ( ! [X412: char,X422: trm] :
% 0.25/0.50 ( Y2
% 0.25/0.50 != ( func @ X412 @ X422 ) )
% 0.25/0.50 => ( ! [X512: trm,X522: trm] :
% 0.25/0.50 ( Y2
% 0.25/0.50 != ( plus @ X512 @ X522 ) )
% 0.25/0.50 => ( ! [X612: trm,X622: trm] :
% 0.25/0.50 ( Y2
% 0.25/0.50 != ( times @ X612 @ X622 ) )
% 0.25/0.50 => ~ ! [X72: trm] :
% 0.25/0.50 ( Y2
% 0.25/0.50 != ( differential @ X72 ) ) ) ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % trm.exhaust
% 0.25/0.50 thf(fact_310_term__sem_Ocases,axiom,
% 0.25/0.50 ! [X2: produc833882726rp_trm] :
% 0.25/0.50 ( ! [I2: denotational_interp,X: variable] :
% 0.25/0.50 ( X2
% 0.25/0.50 != ( produc1132922070rp_trm @ I2 @ ( var @ X ) ) )
% 0.25/0.50 => ( ! [I2: denotational_interp,R5: real] :
% 0.25/0.50 ( X2
% 0.25/0.50 != ( produc1132922070rp_trm @ I2 @ ( number @ R5 ) ) )
% 0.25/0.50 => ( ! [I2: denotational_interp,F3: char] :
% 0.25/0.50 ( X2
% 0.25/0.50 != ( produc1132922070rp_trm @ I2 @ ( const @ F3 ) ) )
% 0.25/0.50 => ( ! [I2: denotational_interp,F3: char,Theta2: trm] :
% 0.25/0.50 ( X2
% 0.25/0.50 != ( produc1132922070rp_trm @ I2 @ ( func @ F3 @ Theta2 ) ) )
% 0.25/0.50 => ( ! [I2: denotational_interp,Theta2: trm,Eta2: trm] :
% 0.25/0.50 ( X2
% 0.25/0.50 != ( produc1132922070rp_trm @ I2 @ ( plus @ Theta2 @ Eta2 ) ) )
% 0.25/0.50 => ( ! [I2: denotational_interp,Theta2: trm,Eta2: trm] :
% 0.25/0.50 ( X2
% 0.25/0.50 != ( produc1132922070rp_trm @ I2 @ ( times @ Theta2 @ Eta2 ) ) )
% 0.25/0.50 => ~ ! [I2: denotational_interp,Theta2: trm] :
% 0.25/0.50 ( X2
% 0.25/0.50 != ( produc1132922070rp_trm @ I2 @ ( differential @ Theta2 ) ) ) ) ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % term_sem.cases
% 0.25/0.50 thf(fact_311_usubstappt_Opsimps_I3_J,axiom,
% 0.25/0.50 ! [Sigma: produc1418842292n_game,U: set_variable,F: char] :
% 0.25/0.50 ( ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ Sigma @ ( produc1482344242le_trm @ U @ ( const @ F ) ) ) )
% 0.25/0.50 => ( ( uSubst516392818stappt @ Sigma @ U @ ( const @ F ) )
% 0.25/0.50 = ( uSubst1559070963pconst @ Sigma @ U @ F ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % usubstappt.psimps(3)
% 0.25/0.50 thf(fact_312_term__sem_Oinduct,axiom,
% 0.25/0.50 ! [P: denotational_interp > trm > $o,A0: denotational_interp,A1: trm] :
% 0.25/0.50 ( ! [I2: denotational_interp,X: variable] : ( P @ I2 @ ( var @ X ) )
% 0.25/0.50 => ( ! [I2: denotational_interp,R5: real] : ( P @ I2 @ ( number @ R5 ) )
% 0.25/0.50 => ( ! [I2: denotational_interp,F3: char] : ( P @ I2 @ ( const @ F3 ) )
% 0.25/0.50 => ( ! [I2: denotational_interp,F3: char,Theta2: trm] :
% 0.25/0.50 ( ( P @ I2 @ Theta2 )
% 0.25/0.50 => ( P @ I2 @ ( func @ F3 @ Theta2 ) ) )
% 0.25/0.50 => ( ! [I2: denotational_interp,Theta2: trm] :
% 0.25/0.50 ( ( P @ I2 @ Theta2 )
% 0.25/0.50 => ! [Eta2: trm] :
% 0.25/0.50 ( ( P @ I2 @ Eta2 )
% 0.25/0.50 => ( P @ I2 @ ( plus @ Theta2 @ Eta2 ) ) ) )
% 0.25/0.50 => ( ! [I2: denotational_interp,Theta2: trm] :
% 0.25/0.50 ( ( P @ I2 @ Theta2 )
% 0.25/0.50 => ! [Eta2: trm] :
% 0.25/0.50 ( ( P @ I2 @ Eta2 )
% 0.25/0.50 => ( P @ I2 @ ( times @ Theta2 @ Eta2 ) ) ) )
% 0.25/0.50 => ( ! [I2: denotational_interp,Theta2: trm] :
% 0.25/0.50 ( ( ? [Xa2: char] :
% 0.25/0.50 ( member_char @ Xa2
% 0.25/0.50 @ ( collect_char
% 0.25/0.50 @ ^ [Uu: char] : $true ) )
% 0.25/0.50 => ( P @ I2 @ Theta2 ) )
% 0.25/0.50 => ( P @ I2 @ ( differential @ Theta2 ) ) )
% 0.25/0.50 => ( P @ A0 @ A1 ) ) ) ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % term_sem.induct
% 0.25/0.50 thf(fact_313_usubstappt_Osimps_I3_J,axiom,
% 0.25/0.50 ! [Sigma: produc1418842292n_game,U: set_variable,F: char] :
% 0.25/0.50 ( ( uSubst516392818stappt @ Sigma @ U @ ( const @ F ) )
% 0.25/0.50 = ( uSubst1559070963pconst @ Sigma @ U @ F ) ) ).
% 0.25/0.50
% 0.25/0.50 % usubstappt.simps(3)
% 0.25/0.50 thf(fact_314_image2__def,axiom,
% 0.25/0.50 ( bNF_Gr2142503190on_fml
% 0.25/0.50 = ( ^ [A2: set_variable,F2: variable > option_game,G: variable > option_fml] :
% 0.25/0.50 ( collec749447393on_fml
% 0.25/0.50 @ ^ [Uu: produc1739631244on_fml] :
% 0.25/0.50 ? [A4: variable] :
% 0.25/0.50 ( ( Uu
% 0.25/0.50 = ( produc2124676926on_fml @ ( F2 @ A4 ) @ ( G @ A4 ) ) )
% 0.25/0.50 & ( member_variable @ A4 @ A2 ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % image2_def
% 0.25/0.50 thf(fact_315_image2__def,axiom,
% 0.25/0.50 ( bNF_Gr756940202on_fml
% 0.25/0.50 = ( ^ [A2: set_char,F2: char > option_game,G: char > option_fml] :
% 0.25/0.50 ( collec749447393on_fml
% 0.25/0.50 @ ^ [Uu: produc1739631244on_fml] :
% 0.25/0.50 ? [A4: char] :
% 0.25/0.50 ( ( Uu
% 0.25/0.50 = ( produc2124676926on_fml @ ( F2 @ A4 ) @ ( G @ A4 ) ) )
% 0.25/0.50 & ( member_char @ A4 @ A2 ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % image2_def
% 0.25/0.50 thf(fact_316_image2__def,axiom,
% 0.25/0.50 ( bNF_Gr400922303on_trm
% 0.25/0.50 = ( ^ [A2: set_variable,F2: variable > option_trm,G: variable > option_trm] :
% 0.25/0.50 ( collec1697116690on_trm
% 0.25/0.50 @ ^ [Uu: produc1072747943on_trm] :
% 0.25/0.50 ? [A4: variable] :
% 0.25/0.50 ( ( Uu
% 0.25/0.50 = ( produc709594775on_trm @ ( F2 @ A4 ) @ ( G @ A4 ) ) )
% 0.25/0.50 & ( member_variable @ A4 @ A2 ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % image2_def
% 0.25/0.50 thf(fact_317_image2__def,axiom,
% 0.25/0.50 ( bNF_Gr1666135339on_trm
% 0.25/0.50 = ( ^ [A2: set_char,F2: char > option_trm,G: char > option_trm] :
% 0.25/0.50 ( collec1697116690on_trm
% 0.25/0.50 @ ^ [Uu: produc1072747943on_trm] :
% 0.25/0.50 ? [A4: char] :
% 0.25/0.50 ( ( Uu
% 0.25/0.50 = ( produc709594775on_trm @ ( F2 @ A4 ) @ ( G @ A4 ) ) )
% 0.25/0.50 & ( member_char @ A4 @ A2 ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % image2_def
% 0.25/0.50 thf(fact_318_image2__def,axiom,
% 0.25/0.50 ( bNF_Gr600956991on_fml
% 0.25/0.50 = ( ^ [A2: set_variable,F2: variable > option_fml,G: variable > option_fml] :
% 0.25/0.50 ( collec670974098on_fml
% 0.25/0.50 @ ^ [Uu: produc46605351on_fml] :
% 0.25/0.50 ? [A4: variable] :
% 0.25/0.50 ( ( Uu
% 0.25/0.50 = ( produc909629463on_fml @ ( F2 @ A4 ) @ ( G @ A4 ) ) )
% 0.25/0.50 & ( member_variable @ A4 @ A2 ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % image2_def
% 0.25/0.50 thf(fact_319_image2__def,axiom,
% 0.25/0.50 ( bNF_Gr1866170027on_fml
% 0.25/0.50 = ( ^ [A2: set_char,F2: char > option_fml,G: char > option_fml] :
% 0.25/0.50 ( collec670974098on_fml
% 0.25/0.50 @ ^ [Uu: produc46605351on_fml] :
% 0.25/0.50 ? [A4: char] :
% 0.25/0.50 ( ( Uu
% 0.25/0.50 = ( produc909629463on_fml @ ( F2 @ A4 ) @ ( G @ A4 ) ) )
% 0.25/0.50 & ( member_char @ A4 @ A2 ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % image2_def
% 0.25/0.50 thf(fact_320_image2__def,axiom,
% 0.25/0.50 ( bNF_Gr1933470746on_trm
% 0.25/0.50 = ( ^ [A2: set_variable,F2: variable > char,G: variable > option_trm] :
% 0.25/0.50 ( collec1756633317on_trm
% 0.25/0.50 @ ^ [Uu: produc464795408on_trm] :
% 0.25/0.50 ? [A4: variable] :
% 0.25/0.50 ( ( Uu
% 0.25/0.50 = ( produc1500300866on_trm @ ( F2 @ A4 ) @ ( G @ A4 ) ) )
% 0.25/0.50 & ( member_variable @ A4 @ A2 ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % image2_def
% 0.25/0.50 thf(fact_321_image2__def,axiom,
% 0.25/0.50 ( bNF_Gr951178926on_trm
% 0.25/0.50 = ( ^ [A2: set_char,F2: char > char,G: char > option_trm] :
% 0.25/0.50 ( collec1756633317on_trm
% 0.25/0.50 @ ^ [Uu: produc464795408on_trm] :
% 0.25/0.50 ? [A4: char] :
% 0.25/0.50 ( ( Uu
% 0.25/0.50 = ( produc1500300866on_trm @ ( F2 @ A4 ) @ ( G @ A4 ) ) )
% 0.25/0.50 & ( member_char @ A4 @ A2 ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % image2_def
% 0.25/0.50 thf(fact_322_image2__def,axiom,
% 0.25/0.50 ( bNF_Gr1330108682le_trm
% 0.25/0.50 = ( ^ [A2: set_variable,F2: variable > set_variable,G: variable > trm] :
% 0.25/0.50 ( collec575343829le_trm
% 0.25/0.50 @ ^ [Uu: produc1367888000le_trm] :
% 0.25/0.50 ? [A4: variable] :
% 0.25/0.50 ( ( Uu
% 0.25/0.50 = ( produc1482344242le_trm @ ( F2 @ A4 ) @ ( G @ A4 ) ) )
% 0.25/0.50 & ( member_variable @ A4 @ A2 ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % image2_def
% 0.25/0.50 thf(fact_323_image2__def,axiom,
% 0.25/0.50 ( bNF_Gr852774302le_trm
% 0.25/0.50 = ( ^ [A2: set_char,F2: char > set_variable,G: char > trm] :
% 0.25/0.50 ( collec575343829le_trm
% 0.25/0.50 @ ^ [Uu: produc1367888000le_trm] :
% 0.25/0.50 ? [A4: char] :
% 0.25/0.50 ( ( Uu
% 0.25/0.50 = ( produc1482344242le_trm @ ( F2 @ A4 ) @ ( G @ A4 ) ) )
% 0.25/0.50 & ( member_char @ A4 @ A2 ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % image2_def
% 0.25/0.50 thf(fact_324_Testo_Oelims,axiom,
% 0.25/0.50 ! [X2: option_fml,Y2: option_game] :
% 0.25/0.50 ( ( ( uSubst1367128042_Testo @ X2 )
% 0.25/0.50 = Y2 )
% 0.25/0.50 => ( ! [Phi2: fml] :
% 0.25/0.50 ( ( X2
% 0.25/0.50 = ( some_fml @ Phi2 ) )
% 0.25/0.50 => ( Y2
% 0.25/0.50 != ( some_game @ ( test @ Phi2 ) ) ) )
% 0.25/0.50 => ~ ( ( X2 = none_fml )
% 0.25/0.50 => ( Y2 != none_game ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % Testo.elims
% 0.25/0.50 thf(fact_325_game_Oinject_I3_J,axiom,
% 0.25/0.50 ! [X32: fml,Y32: fml] :
% 0.25/0.50 ( ( ( test @ X32 )
% 0.25/0.50 = ( test @ Y32 ) )
% 0.25/0.50 = ( X32 = Y32 ) ) ).
% 0.25/0.50
% 0.25/0.50 % game.inject(3)
% 0.25/0.50 thf(fact_326_image2__eqI,axiom,
% 0.25/0.50 ! [B3: option_game,F: variable > option_game,X2: variable,C: option_fml,G2: variable > option_fml,A: set_variable] :
% 0.25/0.50 ( ( B3
% 0.25/0.50 = ( F @ X2 ) )
% 0.25/0.50 => ( ( C
% 0.25/0.50 = ( G2 @ X2 ) )
% 0.25/0.50 => ( ( member_variable @ X2 @ A )
% 0.25/0.50 => ( member1883102883on_fml @ ( produc2124676926on_fml @ B3 @ C ) @ ( bNF_Gr2142503190on_fml @ A @ F @ G2 ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % image2_eqI
% 0.25/0.50 thf(fact_327_image2__eqI,axiom,
% 0.25/0.50 ! [B3: option_game,F: char > option_game,X2: char,C: option_fml,G2: char > option_fml,A: set_char] :
% 0.25/0.50 ( ( B3
% 0.25/0.50 = ( F @ X2 ) )
% 0.25/0.50 => ( ( C
% 0.25/0.50 = ( G2 @ X2 ) )
% 0.25/0.50 => ( ( member_char @ X2 @ A )
% 0.25/0.50 => ( member1883102883on_fml @ ( produc2124676926on_fml @ B3 @ C ) @ ( bNF_Gr756940202on_fml @ A @ F @ G2 ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % image2_eqI
% 0.25/0.50 thf(fact_328_image2__eqI,axiom,
% 0.25/0.50 ! [B3: option_trm,F: variable > option_trm,X2: variable,C: option_trm,G2: variable > option_trm,A: set_variable] :
% 0.25/0.50 ( ( B3
% 0.25/0.50 = ( F @ X2 ) )
% 0.25/0.50 => ( ( C
% 0.25/0.50 = ( G2 @ X2 ) )
% 0.25/0.50 => ( ( member_variable @ X2 @ A )
% 0.25/0.50 => ( member165817296on_trm @ ( produc709594775on_trm @ B3 @ C ) @ ( bNF_Gr400922303on_trm @ A @ F @ G2 ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % image2_eqI
% 0.25/0.50 thf(fact_329_image2__eqI,axiom,
% 0.25/0.50 ! [B3: option_trm,F: char > option_trm,X2: char,C: option_trm,G2: char > option_trm,A: set_char] :
% 0.25/0.50 ( ( B3
% 0.25/0.50 = ( F @ X2 ) )
% 0.25/0.50 => ( ( C
% 0.25/0.50 = ( G2 @ X2 ) )
% 0.25/0.50 => ( ( member_char @ X2 @ A )
% 0.25/0.50 => ( member165817296on_trm @ ( produc709594775on_trm @ B3 @ C ) @ ( bNF_Gr1666135339on_trm @ A @ F @ G2 ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % image2_eqI
% 0.25/0.50 thf(fact_330_image2__eqI,axiom,
% 0.25/0.50 ! [B3: option_fml,F: variable > option_fml,X2: variable,C: option_fml,G2: variable > option_fml,A: set_variable] :
% 0.25/0.50 ( ( B3
% 0.25/0.50 = ( F @ X2 ) )
% 0.25/0.50 => ( ( C
% 0.25/0.50 = ( G2 @ X2 ) )
% 0.25/0.50 => ( ( member_variable @ X2 @ A )
% 0.25/0.50 => ( member1287158352on_fml @ ( produc909629463on_fml @ B3 @ C ) @ ( bNF_Gr600956991on_fml @ A @ F @ G2 ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % image2_eqI
% 0.25/0.50 thf(fact_331_image2__eqI,axiom,
% 0.25/0.50 ! [B3: option_fml,F: char > option_fml,X2: char,C: option_fml,G2: char > option_fml,A: set_char] :
% 0.25/0.50 ( ( B3
% 0.25/0.50 = ( F @ X2 ) )
% 0.25/0.50 => ( ( C
% 0.25/0.50 = ( G2 @ X2 ) )
% 0.25/0.50 => ( ( member_char @ X2 @ A )
% 0.25/0.50 => ( member1287158352on_fml @ ( produc909629463on_fml @ B3 @ C ) @ ( bNF_Gr1866170027on_fml @ A @ F @ G2 ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % image2_eqI
% 0.25/0.50 thf(fact_332_image2__eqI,axiom,
% 0.25/0.50 ! [B3: char,F: variable > char,X2: variable,C: option_trm,G2: variable > option_trm,A: set_variable] :
% 0.25/0.50 ( ( B3
% 0.25/0.50 = ( F @ X2 ) )
% 0.25/0.50 => ( ( C
% 0.25/0.50 = ( G2 @ X2 ) )
% 0.25/0.50 => ( ( member_variable @ X2 @ A )
% 0.25/0.50 => ( member694524327on_trm @ ( produc1500300866on_trm @ B3 @ C ) @ ( bNF_Gr1933470746on_trm @ A @ F @ G2 ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % image2_eqI
% 0.25/0.50 thf(fact_333_image2__eqI,axiom,
% 0.25/0.50 ! [B3: char,F: char > char,X2: char,C: option_trm,G2: char > option_trm,A: set_char] :
% 0.25/0.50 ( ( B3
% 0.25/0.50 = ( F @ X2 ) )
% 0.25/0.50 => ( ( C
% 0.25/0.50 = ( G2 @ X2 ) )
% 0.25/0.50 => ( ( member_char @ X2 @ A )
% 0.25/0.50 => ( member694524327on_trm @ ( produc1500300866on_trm @ B3 @ C ) @ ( bNF_Gr951178926on_trm @ A @ F @ G2 ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % image2_eqI
% 0.25/0.50 thf(fact_334_image2__eqI,axiom,
% 0.25/0.50 ! [B3: set_variable,F: variable > set_variable,X2: variable,C: trm,G2: variable > trm,A: set_variable] :
% 0.25/0.50 ( ( B3
% 0.25/0.50 = ( F @ X2 ) )
% 0.25/0.50 => ( ( C
% 0.25/0.50 = ( G2 @ X2 ) )
% 0.25/0.50 => ( ( member_variable @ X2 @ A )
% 0.25/0.50 => ( member2122665623le_trm @ ( produc1482344242le_trm @ B3 @ C ) @ ( bNF_Gr1330108682le_trm @ A @ F @ G2 ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % image2_eqI
% 0.25/0.50 thf(fact_335_image2__eqI,axiom,
% 0.25/0.50 ! [B3: set_variable,F: char > set_variable,X2: char,C: trm,G2: char > trm,A: set_char] :
% 0.25/0.50 ( ( B3
% 0.25/0.50 = ( F @ X2 ) )
% 0.25/0.50 => ( ( C
% 0.25/0.50 = ( G2 @ X2 ) )
% 0.25/0.50 => ( ( member_char @ X2 @ A )
% 0.25/0.50 => ( member2122665623le_trm @ ( produc1482344242le_trm @ B3 @ C ) @ ( bNF_Gr852774302le_trm @ A @ F @ G2 ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % image2_eqI
% 0.25/0.50 thf(fact_336_Testo_Osimps_I1_J,axiom,
% 0.25/0.50 ! [Phi: fml] :
% 0.25/0.50 ( ( uSubst1367128042_Testo @ ( some_fml @ Phi ) )
% 0.25/0.50 = ( some_game @ ( test @ Phi ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % Testo.simps(1)
% 0.25/0.50 thf(fact_337_Testo_Opelims,axiom,
% 0.25/0.50 ! [X2: option_fml,Y2: option_game] :
% 0.25/0.50 ( ( ( uSubst1367128042_Testo @ X2 )
% 0.25/0.50 = Y2 )
% 0.25/0.50 => ( ( accp_option_fml @ uSubst954181007to_rel @ X2 )
% 0.25/0.50 => ( ! [Phi2: fml] :
% 0.25/0.50 ( ( X2
% 0.25/0.50 = ( some_fml @ Phi2 ) )
% 0.25/0.50 => ( ( Y2
% 0.25/0.50 = ( some_game @ ( test @ Phi2 ) ) )
% 0.25/0.50 => ~ ( accp_option_fml @ uSubst954181007to_rel @ ( some_fml @ Phi2 ) ) ) )
% 0.25/0.50 => ~ ( ( X2 = none_fml )
% 0.25/0.50 => ( ( Y2 = none_game )
% 0.25/0.50 => ~ ( accp_option_fml @ uSubst954181007to_rel @ none_fml ) ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % Testo.pelims
% 0.25/0.50 thf(fact_338_relImage__def,axiom,
% 0.25/0.50 ( bNF_Gr806120164on_fml
% 0.25/0.50 = ( ^ [R6: set_Pr927595527on_fml,F2: option_fml > option_fml] :
% 0.25/0.50 ( collec670974098on_fml
% 0.25/0.50 @ ^ [Uu: produc46605351on_fml] :
% 0.25/0.50 ? [A12: option_fml,A22: option_fml] :
% 0.25/0.50 ( ( Uu
% 0.25/0.50 = ( produc909629463on_fml @ ( F2 @ A12 ) @ ( F2 @ A22 ) ) )
% 0.25/0.50 & ( member1287158352on_fml @ ( produc909629463on_fml @ A12 @ A22 ) @ R6 ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % relImage_def
% 0.25/0.50 thf(fact_339_Assigno__undef,axiom,
% 0.25/0.50 ! [X2: variable,Theta: option_trm] :
% 0.25/0.50 ( ( ( uSubst834381837ssigno @ X2 @ Theta )
% 0.25/0.50 = none_game )
% 0.25/0.50 = ( Theta = none_trm ) ) ).
% 0.25/0.50
% 0.25/0.50 % Assigno_undef
% 0.25/0.50 thf(fact_340_Assigno_Osimps_I2_J,axiom,
% 0.25/0.50 ! [X2: variable] :
% 0.25/0.50 ( ( uSubst834381837ssigno @ X2 @ none_trm )
% 0.25/0.50 = none_game ) ).
% 0.25/0.50
% 0.25/0.50 % Assigno.simps(2)
% 0.25/0.50 thf(fact_341_Assigno_Oelims,axiom,
% 0.25/0.50 ! [X2: variable,Xa: option_trm,Y2: option_game] :
% 0.25/0.50 ( ( ( uSubst834381837ssigno @ X2 @ Xa )
% 0.25/0.50 = Y2 )
% 0.25/0.50 => ( ! [Theta2: trm] :
% 0.25/0.50 ( ( Xa
% 0.25/0.50 = ( some_trm @ Theta2 ) )
% 0.25/0.50 => ( Y2
% 0.25/0.50 != ( some_game @ ( assign @ X2 @ Theta2 ) ) ) )
% 0.25/0.50 => ~ ( ( Xa = none_trm )
% 0.25/0.50 => ( Y2 != none_game ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % Assigno.elims
% 0.25/0.50 thf(fact_342_Assigno_Opelims,axiom,
% 0.25/0.50 ! [X2: variable,Xa: option_trm,Y2: option_game] :
% 0.25/0.50 ( ( ( uSubst834381837ssigno @ X2 @ Xa )
% 0.25/0.50 = Y2 )
% 0.25/0.50 => ( ( accp_P394694195on_trm @ uSubst157155628no_rel @ ( produc1743721902on_trm @ X2 @ Xa ) )
% 0.25/0.50 => ( ! [Theta2: trm] :
% 0.25/0.50 ( ( Xa
% 0.25/0.50 = ( some_trm @ Theta2 ) )
% 0.25/0.50 => ( ( Y2
% 0.25/0.50 = ( some_game @ ( assign @ X2 @ Theta2 ) ) )
% 0.25/0.50 => ~ ( accp_P394694195on_trm @ uSubst157155628no_rel @ ( produc1743721902on_trm @ X2 @ ( some_trm @ Theta2 ) ) ) ) )
% 0.25/0.50 => ~ ( ( Xa = none_trm )
% 0.25/0.50 => ( ( Y2 = none_game )
% 0.25/0.50 => ~ ( accp_P394694195on_trm @ uSubst157155628no_rel @ ( produc1743721902on_trm @ X2 @ none_trm ) ) ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % Assigno.pelims
% 0.25/0.50 thf(fact_343_game_Oinject_I2_J,axiom,
% 0.25/0.50 ! [X21: variable,X22: trm,Y21: variable,Y22: trm] :
% 0.25/0.50 ( ( ( assign @ X21 @ X22 )
% 0.25/0.50 = ( assign @ Y21 @ Y22 ) )
% 0.25/0.50 = ( ( X21 = Y21 )
% 0.25/0.50 & ( X22 = Y22 ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % game.inject(2)
% 0.25/0.50 thf(fact_344_game_Odistinct_I15_J,axiom,
% 0.25/0.50 ! [X21: variable,X22: trm,X32: fml] :
% 0.25/0.50 ( ( assign @ X21 @ X22 )
% 0.25/0.50 != ( test @ X32 ) ) ).
% 0.25/0.50
% 0.25/0.50 % game.distinct(15)
% 0.25/0.50 thf(fact_345_Assigno_Osimps_I1_J,axiom,
% 0.25/0.50 ! [X2: variable,Theta: trm] :
% 0.25/0.50 ( ( uSubst834381837ssigno @ X2 @ ( some_trm @ Theta ) )
% 0.25/0.50 = ( some_game @ ( assign @ X2 @ Theta ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % Assigno.simps(1)
% 0.25/0.50 thf(fact_346_ODEo__undef,axiom,
% 0.25/0.50 ! [X2: char,Theta: option_trm] :
% 0.25/0.50 ( ( ( uSubst1827052306e_ODEo @ X2 @ Theta )
% 0.25/0.50 = none_game )
% 0.25/0.50 = ( Theta = none_trm ) ) ).
% 0.25/0.50
% 0.25/0.50 % ODEo_undef
% 0.25/0.50 thf(fact_347_ODEo_Osimps_I2_J,axiom,
% 0.25/0.50 ! [X2: char] :
% 0.25/0.50 ( ( uSubst1827052306e_ODEo @ X2 @ none_trm )
% 0.25/0.50 = none_game ) ).
% 0.25/0.50
% 0.25/0.50 % ODEo.simps(2)
% 0.25/0.50 thf(fact_348_ODEo_Oelims,axiom,
% 0.25/0.50 ! [X2: char,Xa: option_trm,Y2: option_game] :
% 0.25/0.50 ( ( ( uSubst1827052306e_ODEo @ X2 @ Xa )
% 0.25/0.50 = Y2 )
% 0.25/0.50 => ( ! [Theta2: trm] :
% 0.25/0.50 ( ( Xa
% 0.25/0.50 = ( some_trm @ Theta2 ) )
% 0.25/0.50 => ( Y2
% 0.25/0.50 != ( some_game @ ( ode @ X2 @ Theta2 ) ) ) )
% 0.25/0.50 => ~ ( ( Xa = none_trm )
% 0.25/0.50 => ( Y2 != none_game ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % ODEo.elims
% 0.25/0.50 thf(fact_349_ODEo_Opelims,axiom,
% 0.25/0.50 ! [X2: char,Xa: option_trm,Y2: option_game] :
% 0.25/0.50 ( ( ( uSubst1827052306e_ODEo @ X2 @ Xa )
% 0.25/0.50 = Y2 )
% 0.25/0.50 => ( ( accp_P419951815on_trm @ uSubst299938919Eo_rel @ ( produc1500300866on_trm @ X2 @ Xa ) )
% 0.25/0.50 => ( ! [Theta2: trm] :
% 0.25/0.50 ( ( Xa
% 0.25/0.50 = ( some_trm @ Theta2 ) )
% 0.25/0.50 => ( ( Y2
% 0.25/0.50 = ( some_game @ ( ode @ X2 @ Theta2 ) ) )
% 0.25/0.50 => ~ ( accp_P419951815on_trm @ uSubst299938919Eo_rel @ ( produc1500300866on_trm @ X2 @ ( some_trm @ Theta2 ) ) ) ) )
% 0.25/0.50 => ~ ( ( Xa = none_trm )
% 0.25/0.50 => ( ( Y2 = none_game )
% 0.25/0.50 => ~ ( accp_P419951815on_trm @ uSubst299938919Eo_rel @ ( produc1500300866on_trm @ X2 @ none_trm ) ) ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % ODEo.pelims
% 0.25/0.50 thf(fact_350_game_Oinject_I8_J,axiom,
% 0.25/0.50 ! [X81: char,X82: trm,Y81: char,Y82: trm] :
% 0.25/0.50 ( ( ( ode @ X81 @ X82 )
% 0.25/0.50 = ( ode @ Y81 @ Y82 ) )
% 0.25/0.50 = ( ( X81 = Y81 )
% 0.25/0.50 & ( X82 = Y82 ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % game.inject(8)
% 0.25/0.50 thf(fact_351_game_Odistinct_I35_J,axiom,
% 0.25/0.50 ! [X32: fml,X81: char,X82: trm] :
% 0.25/0.50 ( ( test @ X32 )
% 0.25/0.50 != ( ode @ X81 @ X82 ) ) ).
% 0.25/0.50
% 0.25/0.50 % game.distinct(35)
% 0.25/0.50
% 0.25/0.50 % Conjectures (1)
% 0.25/0.50 thf(conj_0,conjecture,
% 0.25/0.50 ( ( uSubst516392818stappt @ sigma @ ua @ theta )
% 0.25/0.50 != none_trm ) ).
% 0.25/0.50
% 0.25/0.50 %------------------------------------------------------------------------------
% 0.25/0.50 ------------------------
% 4.20/2.09 ---- Embedded in THF ---
% 4.20/2.09 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 4.20/2.09 %%% Generated on Tue Feb 24 08:36:42 EST 2026
% 4.20/2.09 %%% using '$$dhol' embedding, version 1.3.0.
% 4.20/2.09 %%% Logic specification used:
% 4.20/2.09 %%% thf(spec, logic, $$dhol).
% 4.20/2.09
% 4.20/2.09 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.Mj9VJvCut7/DTF2DTF26624.p
% See solution above
% 4.20/2.09 ------------------------
% 4.36/2.17 ---- Cleaned THF ---
% 4.36/2.17 thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_I_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ofml_J_J_M_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ogame_J_J_J_J_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Syntax__Otrm_J_J,type,
% 4.36/2.17 produc1699626005le_trm: $tType ).
% 4.36/2.17
% 4.36/2.17 thf(ty_n_t__Product____Type__Oprod_I_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ofml_J_J_M_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ogame_J_J_J_J_J,type,
% 4.36/2.17 produc1418842292n_game: $tType ).
% 4.36/2.17
% 4.36/2.17 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ogame_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J_Mt__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ogame_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J_J_J,type,
% 4.36/2.17 set_Pr1918373977on_fml: $tType ).
% 4.36/2.17
% 4.36/2.17 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Otrm_J_Mt__Option__Ooption_It__Syntax__Otrm_J_J_Mt__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Otrm_J_Mt__Option__Ooption_It__Syntax__Otrm_J_J_J_J,type,
% 4.36/2.17 set_Pr1062384839on_trm: $tType ).
% 4.36/2.17
% 4.36/2.17 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Otrm_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J_Mt__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Otrm_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J_J_J,type,
% 4.36/2.17 set_Pr519625031on_fml: $tType ).
% 4.36/2.17
% 4.36/2.17 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ofml_J_Mt__Option__Ooption_It__Syntax__Otrm_J_J_Mt__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ofml_J_Mt__Option__Ooption_It__Syntax__Otrm_J_J_J_J,type,
% 4.36/2.17 set_Pr1588097095on_trm: $tType ).
% 4.36/2.17
% 4.36/2.17 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ofml_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J_Mt__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ofml_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J_J_J,type,
% 4.36/2.17 set_Pr1045337287on_fml: $tType ).
% 4.36/2.17
% 4.36/2.17 thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ogame_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J_Mt__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ogame_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J_J,type,
% 4.36/2.17 produc1928189433on_fml: $tType ).
% 4.36/2.17
% 4.36/2.17 thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Otrm_J_Mt__Option__Ooption_It__Syntax__Otrm_J_J_Mt__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Otrm_J_Mt__Option__Ooption_It__Syntax__Otrm_J_J_J,type,
% 4.36/2.17 produc2024965863on_trm: $tType ).
% 4.36/2.17
% 4.36/2.17 thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Otrm_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J_Mt__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Otrm_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J_J,type,
% 4.36/2.17 produc591588199on_fml: $tType ).
% 4.36/2.17
% 4.36/2.17 thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ofml_J_Mt__Option__Ooption_It__Syntax__Otrm_J_J_Mt__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ofml_J_Mt__Option__Ooption_It__Syntax__Otrm_J_J_J,type,
% 4.36/2.17 produc1158546023on_trm: $tType ).
% 4.36/2.17
% 4.36/2.17 thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ofml_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J_Mt__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ofml_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J_J,type,
% 4.36/2.17 produc1872652007on_fml: $tType ).
% 4.36/2.17
% 4.36/2.17 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_Mt__Product____Type__Oprod_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_J_J,type,
% 4.36/2.17 set_Pr1481565921on_trm: $tType ).
% 4.36/2.17
% 4.36/2.17 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Syntax__Otrm_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Syntax__Otrm_J_J_J,type,
% 4.36/2.17 set_Pr1969262145le_trm: $tType ).
% 4.36/2.17
% 4.36/2.17 thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_Mt__Product____Type__Oprod_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_J,type,
% 4.36/2.17 produc2018724225on_trm: $tType ).
% 4.36/2.17
% 4.36/2.17 thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Syntax__Otrm_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Syntax__Otrm_J_J,type,
% 4.36/2.17 produc1279577057le_trm: $tType ).
% 4.36/2.17
% 4.36/2.17 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ogame_J_Mt__Option__Ooption_It__Syntax__Ogame_J_J_J,type,
% 4.36/2.17 set_Pr1625152599n_game: $tType ).
% 4.36/2.17
% 4.36/2.17 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ogame_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J_J,type,
% 4.36/2.17 set_Pr622314946on_fml: $tType ).
% 4.36/2.17
% 4.36/2.17 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Otrm_J_Mt__Option__Ooption_It__Syntax__Otrm_J_J_J,type,
% 4.36/2.17 set_Pr1471344007on_trm: $tType ).
% 4.36/2.17
% 4.36/2.17 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ofml_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J_J,type,
% 4.36/2.17 set_Pr927595527on_fml: $tType ).
% 4.36/2.17
% 4.36/2.17 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Set__Oset_It__Syntax__Ovariable_J_J_J,type,
% 4.36/2.17 set_Pr181266295riable: $tType ).
% 4.36/2.17
% 4.36/2.17 thf(ty_n_t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ogame_J_Mt__Option__Ooption_It__Syntax__Ogame_J_J,type,
% 4.36/2.17 produc1016592119n_game: $tType ).
% 4.36/2.17
% 4.36/2.17 thf(ty_n_t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ogame_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J,type,
% 4.36/2.17 produc1739631244on_fml: $tType ).
% 4.36/2.17
% 4.36/2.17 thf(ty_n_t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Otrm_J_Mt__Option__Ooption_It__Syntax__Otrm_J_J,type,
% 4.36/2.17 produc1072747943on_trm: $tType ).
% 4.36/2.17
% 4.36/2.17 thf(ty_n_t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Otrm_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J,type,
% 4.36/2.17 produc1456309597on_fml: $tType ).
% 4.36/2.17
% 4.36/2.17 thf(ty_n_t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ofml_J_Mt__Option__Ooption_It__Syntax__Otrm_J_J,type,
% 4.36/2.17 produc1810527345on_trm: $tType ).
% 4.36/2.17
% 4.36/2.17 thf(ty_n_t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ofml_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J,type,
% 4.36/2.17 produc46605351on_fml: $tType ).
% 4.36/2.17
% 4.36/2.17 thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Set__Oset_It__Syntax__Ovariable_J_J,type,
% 4.36/2.17 produc432717079riable: $tType ).
% 4.36/2.17
% 4.36/2.17 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_J,type,
% 4.36/2.17 set_Pr943832262on_trm: $tType ).
% 4.36/2.17
% 4.36/2.17 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Syntax__Otrm_J_J,type,
% 4.36/2.17 set_Pr1235432374le_trm: $tType ).
% 4.36/2.17
% 4.36/2.17 thf(ty_n_t__Product____Type__Oprod_It__Syntax__Ovariable_Mt__Option__Ooption_It__Syntax__Otrm_J_J,type,
% 4.36/2.17 produc1024976764on_trm: $tType ).
% 4.36/2.17
% 4.36/2.17 thf(ty_n_t__Product____Type__Oprod_It__Syntax__Ovariable_Mt__Option__Ooption_It__Syntax__Ofml_J_J,type,
% 4.36/2.17 produc1408538418on_fml: $tType ).
% 4.36/2.17
% 4.36/2.17 thf(ty_n_t__Product____Type__Oprod_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J,type,
% 4.36/2.17 produc464795408on_trm: $tType ).
% 4.36/2.17
% 4.36/2.17 thf(ty_n_t__Product____Type__Oprod_It__Denotational____Semantics__Ointerp_Mt__Syntax__Otrm_J,type,
% 4.36/2.17 produc833882726rp_trm: $tType ).
% 4.36/2.17
% 4.36/2.17 thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Syntax__Otrm_J,type,
% 4.36/2.17 produc1367888000le_trm: $tType ).
% 4.36/2.17
% 4.36/2.17 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__String__Ochar_Mt__String__Ochar_J_J,type,
% 4.36/2.17 set_Pr604539619r_char: $tType ).
% 4.36/2.17
% 4.36/2.17 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Syntax__Otrm_Mt__Syntax__Otrm_J_J,type,
% 4.36/2.17 set_Pr491793543rm_trm: $tType ).
% 4.36/2.17
% 4.36/2.17 thf(ty_n_t__Product____Type__Oprod_It__String__Ochar_Mt__String__Ochar_J,type,
% 4.36/2.17 produc1593312387r_char: $tType ).
% 4.36/2.17
% 4.36/2.17 thf(ty_n_t__Product____Type__Oprod_It__Syntax__Otrm_Mt__Syntax__Otrm_J,type,
% 4.36/2.17 product_prod_trm_trm: $tType ).
% 4.36/2.17
% 4.36/2.17 thf(ty_n_t__Option__Ooption_It__Syntax__Ogame_J,type,
% 4.36/2.17 option_game: $tType ).
% 4.36/2.17
% 4.36/2.17 thf(ty_n_t__Option__Ooption_It__Syntax__Otrm_J,type,
% 4.36/2.17 option_trm: $tType ).
% 4.36/2.17
% 4.36/2.17 thf(ty_n_t__Option__Ooption_It__Syntax__Ofml_J,type,
% 4.36/2.17 option_fml: $tType ).
% 4.36/2.17
% 4.36/2.17 thf(ty_n_t__Denotational____Semantics__Ointerp,type,
% 4.36/2.17 denotational_interp: $tType ).
% 4.36/2.17
% 4.36/2.17 thf(ty_n_t__Set__Oset_It__Syntax__Ovariable_J,type,
% 4.36/2.17 set_variable: $tType ).
% 4.36/2.17
% 4.36/2.17 thf(ty_n_t__Set__Oset_It__String__Ochar_J,type,
% 4.36/2.17 set_char: $tType ).
% 4.36/2.17
% 4.36/2.17 thf(ty_n_t__Syntax__Ovariable,type,
% 4.36/2.17 variable: $tType ).
% 4.36/2.17
% 4.36/2.17 thf(ty_n_t__Syntax__Ogame,type,
% 4.36/2.17 game: $tType ).
% 4.36/2.17
% 4.36/2.17 thf(ty_n_t__String__Ochar,type,
% 4.36/2.17 char: $tType ).
% 4.36/2.17
% 4.36/2.17 thf(ty_n_t__Syntax__Otrm,type,
% 4.36/2.17 trm: $tType ).
% 4.36/2.17
% 4.36/2.17 thf(ty_n_t__Syntax__Ofml,type,
% 4.36/2.17 fml: $tType ).
% 4.36/2.17
% 4.36/2.17 thf(ty_n_t__Real__Oreal,type,
% 4.36/2.17 real: $tType ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001t__String__Ochar_001t__Option__Ooption_It__Syntax__Ofml_J_001t__Option__Ooption_It__Syntax__Ofml_J,type,
% 4.36/2.17 bNF_Gr1866170027on_fml: set_char > ( char > option_fml ) > ( char > option_fml ) > set_Pr927595527on_fml ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001t__String__Ochar_001t__Option__Ooption_It__Syntax__Ogame_J_001t__Option__Ooption_It__Syntax__Ofml_J,type,
% 4.36/2.17 bNF_Gr756940202on_fml: set_char > ( char > option_game ) > ( char > option_fml ) > set_Pr622314946on_fml ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001t__String__Ochar_001t__Option__Ooption_It__Syntax__Otrm_J_001t__Option__Ooption_It__Syntax__Otrm_J,type,
% 4.36/2.17 bNF_Gr1666135339on_trm: set_char > ( char > option_trm ) > ( char > option_trm ) > set_Pr1471344007on_trm ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001t__String__Ochar_001t__Set__Oset_It__Syntax__Ovariable_J_001t__Syntax__Otrm,type,
% 4.36/2.17 bNF_Gr852774302le_trm: set_char > ( char > set_variable ) > ( char > trm ) > set_Pr1235432374le_trm ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001t__String__Ochar_001t__String__Ochar_001t__Option__Ooption_It__Syntax__Otrm_J,type,
% 4.36/2.17 bNF_Gr951178926on_trm: set_char > ( char > char ) > ( char > option_trm ) > set_Pr943832262on_trm ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001t__Syntax__Ovariable_001t__Option__Ooption_It__Syntax__Ofml_J_001t__Option__Ooption_It__Syntax__Ofml_J,type,
% 4.36/2.17 bNF_Gr600956991on_fml: set_variable > ( variable > option_fml ) > ( variable > option_fml ) > set_Pr927595527on_fml ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001t__Syntax__Ovariable_001t__Option__Ooption_It__Syntax__Ogame_J_001t__Option__Ooption_It__Syntax__Ofml_J,type,
% 4.36/2.17 bNF_Gr2142503190on_fml: set_variable > ( variable > option_game ) > ( variable > option_fml ) > set_Pr622314946on_fml ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001t__Syntax__Ovariable_001t__Option__Ooption_It__Syntax__Otrm_J_001t__Option__Ooption_It__Syntax__Otrm_J,type,
% 4.36/2.17 bNF_Gr400922303on_trm: set_variable > ( variable > option_trm ) > ( variable > option_trm ) > set_Pr1471344007on_trm ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001t__Syntax__Ovariable_001t__Set__Oset_It__Syntax__Ovariable_J_001t__Syntax__Otrm,type,
% 4.36/2.17 bNF_Gr1330108682le_trm: set_variable > ( variable > set_variable ) > ( variable > trm ) > set_Pr1235432374le_trm ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001t__Syntax__Ovariable_001t__String__Ochar_001t__Option__Ooption_It__Syntax__Otrm_J,type,
% 4.36/2.17 bNF_Gr1933470746on_trm: set_variable > ( variable > char ) > ( variable > option_trm ) > set_Pr943832262on_trm ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_BNF__Greatest__Fixpoint_OrelImage_001t__Option__Ooption_It__Syntax__Ofml_J_001t__Option__Ooption_It__Syntax__Ofml_J,type,
% 4.36/2.17 bNF_Gr806120164on_fml: set_Pr927595527on_fml > ( option_fml > option_fml ) > set_Pr927595527on_fml ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_Denotational__Semantics_OUvariation,type,
% 4.36/2.17 denota1419872369iation: ( variable > real ) > ( variable > real ) > set_variable > $o ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_Option_Ooption_ONone_001t__Syntax__Ofml,type,
% 4.36/2.17 none_fml: option_fml ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_Option_Ooption_ONone_001t__Syntax__Ogame,type,
% 4.36/2.17 none_game: option_game ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_Option_Ooption_ONone_001t__Syntax__Otrm,type,
% 4.36/2.17 none_trm: option_trm ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_Option_Ooption_OSome_001t__Syntax__Ofml,type,
% 4.36/2.17 some_fml: fml > option_fml ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_Option_Ooption_OSome_001t__Syntax__Ogame,type,
% 4.36/2.17 some_game: game > option_game ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_Option_Ooption_OSome_001t__Syntax__Otrm,type,
% 4.36/2.17 some_trm: trm > option_trm ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_Option_Ooption_Ocase__option_001_Eo_001t__Syntax__Ofml,type,
% 4.36/2.17 case_option_o_fml: $o > ( fml > $o ) > option_fml > $o ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_Option_Ooption_Ocase__option_001_Eo_001t__Syntax__Ogame,type,
% 4.36/2.17 case_option_o_game: $o > ( game > $o ) > option_game > $o ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_Option_Ooption_Ocase__option_001_Eo_001t__Syntax__Otrm,type,
% 4.36/2.17 case_option_o_trm: $o > ( trm > $o ) > option_trm > $o ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_Option_Ooption_Othe_001t__Syntax__Ofml,type,
% 4.36/2.17 the_fml: option_fml > fml ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_Option_Ooption_Othe_001t__Syntax__Ogame,type,
% 4.36/2.17 the_game: option_game > game ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_Option_Ooption_Othe_001t__Syntax__Otrm,type,
% 4.36/2.17 the_trm: option_trm > trm ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Option__Ooption_It__Syntax__Ofml_J_M_062_It__Option__Ooption_It__Syntax__Ofml_J_M_Eo_J_J,type,
% 4.36/2.17 ord_le802833166_fml_o: ( option_fml > option_fml > $o ) > ( option_fml > option_fml > $o ) > $o ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Option__Ooption_It__Syntax__Ofml_J_M_Eo_J,type,
% 4.36/2.17 ord_le181580155_fml_o: ( option_fml > $o ) > ( option_fml > $o ) > $o ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Option__Ooption_It__Syntax__Ogame_J_M_062_It__Option__Ooption_It__Syntax__Ofml_J_M_Eo_J_J,type,
% 4.36/2.17 ord_le1588489637_fml_o: ( option_game > option_fml > $o ) > ( option_game > option_fml > $o ) > $o ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Option__Ooption_It__Syntax__Otrm_J_M_062_It__Option__Ooption_It__Syntax__Otrm_J_M_Eo_J_J,type,
% 4.36/2.17 ord_le847028878_trm_o: ( option_trm > option_trm > $o ) > ( option_trm > option_trm > $o ) > $o ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Option__Ooption_It__Syntax__Otrm_J_M_Eo_J,type,
% 4.36/2.17 ord_le1957133745_trm_o: ( option_trm > $o ) > ( option_trm > $o ) > $o ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Otrm_J_Mt__Option__Ooption_It__Syntax__Otrm_J_J_M_062_It__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Otrm_J_Mt__Option__Ooption_It__Syntax__Otrm_J_J_M_Eo_J_J,type,
% 4.36/2.17 ord_le90123726_trm_o: ( produc1072747943on_trm > produc1072747943on_trm > $o ) > ( produc1072747943on_trm > produc1072747943on_trm > $o ) > $o ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Otrm_J_Mt__Option__Ooption_It__Syntax__Otrm_J_J_M_Eo_J,type,
% 4.36/2.17 ord_le1721128566_trm_o: ( produc1072747943on_trm > $o ) > ( produc1072747943on_trm > $o ) > $o ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Product____Type__Oprod_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_M_062_It__Product____Type__Oprod_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_M_Eo_J_J,type,
% 4.36/2.17 ord_le157637894_trm_o: ( produc464795408on_trm > produc464795408on_trm > $o ) > ( produc464795408on_trm > produc464795408on_trm > $o ) > $o ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Product____Type__Oprod_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_M_Eo_J,type,
% 4.36/2.17 ord_le1222882015_trm_o: ( produc464795408on_trm > $o ) > ( produc464795408on_trm > $o ) > $o ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Product____Type__Oprod_It__Syntax__Ovariable_Mt__Option__Ooption_It__Syntax__Otrm_J_J_M_062_It__Product____Type__Oprod_It__Syntax__Ovariable_Mt__Option__Ooption_It__Syntax__Otrm_J_J_M_Eo_J_J,type,
% 4.36/2.17 ord_le370603054_trm_o: ( produc1024976764on_trm > produc1024976764on_trm > $o ) > ( produc1024976764on_trm > produc1024976764on_trm > $o ) > $o ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Product____Type__Oprod_It__Syntax__Ovariable_Mt__Option__Ooption_It__Syntax__Otrm_J_J_M_Eo_J,type,
% 4.36/2.17 ord_le373274227_trm_o: ( produc1024976764on_trm > $o ) > ( produc1024976764on_trm > $o ) > $o ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Set__Oset_It__Syntax__Ovariable_J_M_062_It__Syntax__Otrm_M_Eo_J_J,type,
% 4.36/2.17 ord_le691957041_trm_o: ( set_variable > trm > $o ) > ( set_variable > trm > $o ) > $o ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__String__Ochar_M_062_It__Option__Ooption_It__Syntax__Otrm_J_M_Eo_J_J,type,
% 4.36/2.17 ord_le1890124833_trm_o: ( char > option_trm > $o ) > ( char > option_trm > $o ) > $o ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__String__Ochar_M_Eo_J,type,
% 4.36/2.17 ord_less_eq_char_o: ( char > $o ) > ( char > $o ) > $o ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Syntax__Ovariable_M_Eo_J,type,
% 4.36/2.17 ord_le1407353162able_o: ( variable > $o ) > ( variable > $o ) > $o ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ofml_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J_J,type,
% 4.36/2.17 ord_le778974119on_fml: set_Pr927595527on_fml > set_Pr927595527on_fml > $o ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ogame_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J_J,type,
% 4.36/2.17 ord_le782333474on_fml: set_Pr622314946on_fml > set_Pr622314946on_fml > $o ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Otrm_J_Mt__Option__Ooption_It__Syntax__Otrm_J_J_J,type,
% 4.36/2.17 ord_le1322722599on_trm: set_Pr1471344007on_trm > set_Pr1471344007on_trm > $o ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Syntax__Otrm_J_J,type,
% 4.36/2.17 ord_le2102862870le_trm: set_Pr1235432374le_trm > set_Pr1235432374le_trm > $o ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_J,type,
% 4.36/2.17 ord_le541293862on_trm: set_Pr943832262on_trm > set_Pr943832262on_trm > $o ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__String__Ochar_J,type,
% 4.36/2.17 ord_less_eq_set_char: set_char > set_char > $o ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Syntax__Ovariable_J,type,
% 4.36/2.17 ord_le282106107riable: set_variable > set_variable > $o ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_Orderings_Oorder__class_OGreatest_001t__Set__Oset_It__Syntax__Ovariable_J,type,
% 4.36/2.17 order_272405634riable: ( set_variable > $o ) > set_variable ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_Product__Type_OPair_001t__Denotational____Semantics__Ointerp_001t__Syntax__Otrm,type,
% 4.36/2.17 produc1132922070rp_trm: denotational_interp > trm > produc833882726rp_trm ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_Product__Type_OPair_001t__Option__Ooption_It__Syntax__Ofml_J_001t__Option__Ooption_It__Syntax__Ofml_J,type,
% 4.36/2.17 produc909629463on_fml: option_fml > option_fml > produc46605351on_fml ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_Product__Type_OPair_001t__Option__Ooption_It__Syntax__Ofml_J_001t__Option__Ooption_It__Syntax__Otrm_J,type,
% 4.36/2.17 produc1447374177on_trm: option_fml > option_trm > produc1810527345on_trm ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_Product__Type_OPair_001t__Option__Ooption_It__Syntax__Ogame_J_001t__Option__Ooption_It__Syntax__Ofml_J,type,
% 4.36/2.17 produc2124676926on_fml: option_game > option_fml > produc1739631244on_fml ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_Product__Type_OPair_001t__Option__Ooption_It__Syntax__Ogame_J_001t__Option__Ooption_It__Syntax__Ogame_J,type,
% 4.36/2.17 produc1111617711n_game: option_game > option_game > produc1016592119n_game ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_Product__Type_OPair_001t__Option__Ooption_It__Syntax__Otrm_J_001t__Option__Ooption_It__Syntax__Ofml_J,type,
% 4.36/2.17 produc171850061on_fml: option_trm > option_fml > produc1456309597on_fml ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_Product__Type_OPair_001t__Option__Ooption_It__Syntax__Otrm_J_001t__Option__Ooption_It__Syntax__Otrm_J,type,
% 4.36/2.17 produc709594775on_trm: option_trm > option_trm > produc1072747943on_trm ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_I_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ofml_J_J_M_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ogame_J_J_J_J_J_001t__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Syntax__Otrm_J,type,
% 4.36/2.17 produc2015636557le_trm: produc1418842292n_game > produc1367888000le_trm > produc1699626005le_trm ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ofml_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J_001t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ofml_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J,type,
% 4.36/2.17 produc1367044951on_fml: produc46605351on_fml > produc46605351on_fml > produc1872652007on_fml ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ofml_J_Mt__Option__Ooption_It__Syntax__Otrm_J_J_001t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ofml_J_Mt__Option__Ooption_It__Syntax__Otrm_J_J,type,
% 4.36/2.17 produc2132972503on_trm: produc1810527345on_trm > produc1810527345on_trm > produc1158546023on_trm ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ogame_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J_001t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ogame_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J,type,
% 4.36/2.17 produc556056113on_fml: produc1739631244on_fml > produc1739631244on_fml > produc1928189433on_fml ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Otrm_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J_001t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Otrm_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J,type,
% 4.36/2.17 produc1235825367on_fml: produc1456309597on_fml > produc1456309597on_fml > produc591588199on_fml ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Otrm_J_Mt__Option__Ooption_It__Syntax__Otrm_J_J_001t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Otrm_J_Mt__Option__Ooption_It__Syntax__Otrm_J_J,type,
% 4.36/2.17 produc2001752919on_trm: produc1072747943on_trm > produc1072747943on_trm > produc2024965863on_trm ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Syntax__Otrm_J_001t__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Syntax__Otrm_J,type,
% 4.36/2.17 produc1056455193le_trm: produc1367888000le_trm > produc1367888000le_trm > produc1279577057le_trm ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_001t__Product____Type__Oprod_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J,type,
% 4.36/2.17 produc444919481on_trm: produc464795408on_trm > produc464795408on_trm > produc2018724225on_trm ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Syntax__Ovariable_J_001t__Set__Oset_It__Syntax__Ovariable_J,type,
% 4.36/2.17 produc1766592463riable: set_variable > set_variable > produc432717079riable ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Syntax__Ovariable_J_001t__Syntax__Otrm,type,
% 4.36/2.17 produc1482344242le_trm: set_variable > trm > produc1367888000le_trm ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_Product__Type_OPair_001t__String__Ochar_001t__Option__Ooption_It__Syntax__Otrm_J,type,
% 4.36/2.17 produc1500300866on_trm: char > option_trm > produc464795408on_trm ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_Product__Type_OPair_001t__String__Ochar_001t__String__Ochar,type,
% 4.36/2.17 produc19545147r_char: char > char > produc1593312387r_char ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_Product__Type_OPair_001t__Syntax__Otrm_001t__Syntax__Otrm,type,
% 4.36/2.17 product_Pair_trm_trm: trm > trm > product_prod_trm_trm ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_Product__Type_OPair_001t__Syntax__Ovariable_001t__Option__Ooption_It__Syntax__Ofml_J,type,
% 4.36/2.17 produc1205977188on_fml: variable > option_fml > produc1408538418on_fml ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_Product__Type_OPair_001t__Syntax__Ovariable_001t__Option__Ooption_It__Syntax__Otrm_J,type,
% 4.36/2.17 produc1743721902on_trm: variable > option_trm > produc1024976764on_trm ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ofml_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J,type,
% 4.36/2.17 collec670974098on_fml: ( produc46605351on_fml > $o ) > set_Pr927595527on_fml ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ogame_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J,type,
% 4.36/2.17 collec749447393on_fml: ( produc1739631244on_fml > $o ) > set_Pr622314946on_fml ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Otrm_J_Mt__Option__Ooption_It__Syntax__Otrm_J_J,type,
% 4.36/2.17 collec1697116690on_trm: ( produc1072747943on_trm > $o ) > set_Pr1471344007on_trm ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Syntax__Otrm_J,type,
% 4.36/2.17 collec575343829le_trm: ( produc1367888000le_trm > $o ) > set_Pr1235432374le_trm ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J,type,
% 4.36/2.17 collec1756633317on_trm: ( produc464795408on_trm > $o ) > set_Pr943832262on_trm ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_Set_OCollect_001t__String__Ochar,type,
% 4.36/2.17 collect_char: ( char > $o ) > set_char ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_Set_OCollect_001t__Syntax__Ovariable,type,
% 4.36/2.17 collect_variable: ( variable > $o ) > set_variable ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_Syntax_Ofml_OGeq,type,
% 4.36/2.17 geq: trm > trm > fml ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_Syntax_Ogame_OAssign,type,
% 4.36/2.17 assign: variable > trm > game ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_Syntax_Ogame_OODE,type,
% 4.36/2.17 ode: char > trm > game ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_Syntax_Ogame_OTest,type,
% 4.36/2.17 test: fml > game ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_Syntax_Otrm_OConst,type,
% 4.36/2.17 const: char > trm ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_Syntax_Otrm_ODifferential,type,
% 4.36/2.17 differential: trm > trm ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_Syntax_Otrm_OFunc,type,
% 4.36/2.17 func: char > trm > trm ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_Syntax_Otrm_ONumber,type,
% 4.36/2.17 number: real > trm ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_Syntax_Otrm_OPlus,type,
% 4.36/2.17 plus: trm > trm > trm ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_Syntax_Otrm_OTimes,type,
% 4.36/2.17 times: trm > trm > trm ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_Syntax_Otrm_OVar,type,
% 4.36/2.17 var: variable > trm ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_OAssigno,type,
% 4.36/2.17 uSubst834381837ssigno: variable > option_trm > option_game ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_OAssigno__rel,type,
% 4.36/2.17 uSubst157155628no_rel: produc1024976764on_trm > produc1024976764on_trm > $o ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_ODifferentialo,type,
% 4.36/2.17 uSubst716837505ntialo: option_trm > option_trm ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_ODifferentialo__rel,type,
% 4.36/2.17 uSubst2051024824lo_rel: option_trm > option_trm > $o ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_OGeqo,type,
% 4.36/2.17 uSubst152838031e_Geqo: option_trm > option_trm > option_fml ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_OGeqo__rel,type,
% 4.36/2.17 uSubst1304144938qo_rel: produc1072747943on_trm > produc1072747943on_trm > $o ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_OODEo,type,
% 4.36/2.17 uSubst1827052306e_ODEo: char > option_trm > option_game ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_OODEo__rel,type,
% 4.36/2.17 uSubst299938919Eo_rel: produc464795408on_trm > produc464795408on_trm > $o ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_OPluso,type,
% 4.36/2.17 uSubst141955042_Pluso: option_trm > option_trm > option_trm ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_OPluso__rel,type,
% 4.36/2.17 uSubst691094423so_rel: produc1072747943on_trm > produc1072747943on_trm > $o ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_OTesto,type,
% 4.36/2.17 uSubst1367128042_Testo: option_fml > option_game ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_OTesto__rel,type,
% 4.36/2.17 uSubst954181007to_rel: option_fml > option_fml > $o ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_OTimeso,type,
% 4.36/2.17 uSubst918876924Timeso: option_trm > option_trm > option_trm ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_OTimeso__rel,type,
% 4.36/2.17 uSubst924844285so_rel: produc1072747943on_trm > produc1072747943on_trm > $o ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_Ousappconst,type,
% 4.36/2.17 uSubst1559070963pconst: produc1418842292n_game > set_variable > char > option_trm ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_Ousubstappf,type,
% 4.36/2.17 uSubst516392804stappf: produc1418842292n_game > set_variable > fml > option_fml ).
% 4.36/2.17
% 4.36/2.17 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_Ousubstappt,type,
% 4.36/2.17 uSubst516392818stappt: produc1418842292n_game > set_variable > trm > option_trm ).
% 4.36/2.18
% 4.36/2.18 thf(sy_c_USubst__Mirabelle__vidvnmlwwz_Ousubstappt__rel,type,
% 4.36/2.18 uSubst1917534215pt_rel: produc1699626005le_trm > produc1699626005le_trm > $o ).
% 4.36/2.18
% 4.36/2.18 thf(sy_c_Wellfounded_Oaccp_001t__Option__Ooption_It__Syntax__Ofml_J,type,
% 4.36/2.18 accp_option_fml: ( option_fml > option_fml > $o ) > option_fml > $o ).
% 4.36/2.18
% 4.36/2.18 thf(sy_c_Wellfounded_Oaccp_001t__Option__Ooption_It__Syntax__Otrm_J,type,
% 4.36/2.18 accp_option_trm: ( option_trm > option_trm > $o ) > option_trm > $o ).
% 4.36/2.18
% 4.36/2.18 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Otrm_J_Mt__Option__Ooption_It__Syntax__Otrm_J_J,type,
% 4.36/2.18 accp_P758790320on_trm: ( produc1072747943on_trm > produc1072747943on_trm > $o ) > produc1072747943on_trm > $o ).
% 4.36/2.18
% 4.36/2.18 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Product____Type__Oprod_I_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_Mt__Product____Type__Oprod_I_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ofml_J_J_M_062_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Ogame_J_J_J_J_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Syntax__Otrm_J_J,type,
% 4.36/2.18 accp_P1877119646le_trm: ( produc1699626005le_trm > produc1699626005le_trm > $o ) > produc1699626005le_trm > $o ).
% 4.36/2.18
% 4.36/2.18 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J,type,
% 4.36/2.18 accp_P419951815on_trm: ( produc464795408on_trm > produc464795408on_trm > $o ) > produc464795408on_trm > $o ).
% 4.36/2.18
% 4.36/2.18 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Syntax__Ovariable_Mt__Option__Ooption_It__Syntax__Otrm_J_J,type,
% 4.36/2.18 accp_P394694195on_trm: ( produc1024976764on_trm > produc1024976764on_trm > $o ) > produc1024976764on_trm > $o ).
% 4.36/2.18
% 4.36/2.18 thf(sy_c_Wellfounded_Olex__prod_001t__Option__Ooption_It__Syntax__Ofml_J_001t__Option__Ooption_It__Syntax__Ofml_J,type,
% 4.36/2.18 lex_pr314879023on_fml: set_Pr927595527on_fml > set_Pr927595527on_fml > set_Pr1045337287on_fml ).
% 4.36/2.18
% 4.36/2.18 thf(sy_c_Wellfounded_Olex__prod_001t__Option__Ooption_It__Syntax__Ofml_J_001t__Option__Ooption_It__Syntax__Otrm_J,type,
% 4.36/2.18 lex_pr852623737on_trm: set_Pr927595527on_fml > set_Pr1471344007on_trm > set_Pr1588097095on_trm ).
% 4.36/2.18
% 4.36/2.18 thf(sy_c_Wellfounded_Olex__prod_001t__Option__Ooption_It__Syntax__Ogame_J_001t__Option__Ooption_It__Syntax__Ofml_J,type,
% 4.36/2.18 lex_pr425996582on_fml: set_Pr1625152599n_game > set_Pr927595527on_fml > set_Pr1918373977on_fml ).
% 4.36/2.18
% 4.36/2.18 thf(sy_c_Wellfounded_Olex__prod_001t__Option__Ooption_It__Syntax__Otrm_J_001t__Option__Ooption_It__Syntax__Ofml_J,type,
% 4.36/2.18 lex_pr1724583269on_fml: set_Pr1471344007on_trm > set_Pr927595527on_fml > set_Pr519625031on_fml ).
% 4.36/2.18
% 4.36/2.18 thf(sy_c_Wellfounded_Olex__prod_001t__Option__Ooption_It__Syntax__Otrm_J_001t__Option__Ooption_It__Syntax__Otrm_J,type,
% 4.36/2.18 lex_pr114844335on_trm: set_Pr1471344007on_trm > set_Pr1471344007on_trm > set_Pr1062384839on_trm ).
% 4.36/2.18
% 4.36/2.18 thf(sy_c_Wellfounded_Olex__prod_001t__Set__Oset_It__Syntax__Ovariable_J_001t__Syntax__Otrm,type,
% 4.36/2.18 lex_pr1522821402le_trm: set_Pr181266295riable > set_Pr491793543rm_trm > set_Pr1969262145le_trm ).
% 4.36/2.18
% 4.36/2.18 thf(sy_c_Wellfounded_Olex__prod_001t__String__Ochar_001t__Option__Ooption_It__Syntax__Otrm_J,type,
% 4.36/2.18 lex_pr1901327402on_trm: set_Pr604539619r_char > set_Pr1471344007on_trm > set_Pr1481565921on_trm ).
% 4.36/2.18
% 4.36/2.18 thf(sy_c_member_001t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ofml_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J,type,
% 4.36/2.18 member1287158352on_fml: produc46605351on_fml > set_Pr927595527on_fml > $o ).
% 4.36/2.18
% 4.36/2.18 thf(sy_c_member_001t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ogame_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J,type,
% 4.36/2.18 member1883102883on_fml: produc1739631244on_fml > set_Pr622314946on_fml > $o ).
% 4.36/2.18
% 4.36/2.18 thf(sy_c_member_001t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ogame_J_Mt__Option__Ooption_It__Syntax__Ogame_J_J,type,
% 4.36/2.18 member191809696n_game: produc1016592119n_game > set_Pr1625152599n_game > $o ).
% 4.36/2.18
% 4.36/2.18 thf(sy_c_member_001t__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Otrm_J_Mt__Option__Ooption_It__Syntax__Otrm_J_J,type,
% 4.36/2.18 member165817296on_trm: produc1072747943on_trm > set_Pr1471344007on_trm > $o ).
% 4.36/2.18
% 4.36/2.18 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ofml_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J_Mt__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ofml_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J_J,type,
% 4.36/2.18 member450497296on_fml: produc1872652007on_fml > set_Pr1045337287on_fml > $o ).
% 4.36/2.18
% 4.36/2.18 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ofml_J_Mt__Option__Ooption_It__Syntax__Otrm_J_J_Mt__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ofml_J_Mt__Option__Ooption_It__Syntax__Otrm_J_J_J,type,
% 4.36/2.18 member1883874960on_trm: produc1158546023on_trm > set_Pr1588097095on_trm > $o ).
% 4.36/2.18
% 4.36/2.18 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ogame_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J_Mt__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Ogame_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J_J,type,
% 4.36/2.18 member113767842on_fml: produc1928189433on_fml > set_Pr1918373977on_fml > $o ).
% 4.36/2.18
% 4.36/2.18 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Otrm_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J_Mt__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Otrm_J_Mt__Option__Ooption_It__Syntax__Ofml_J_J_J,type,
% 4.36/2.18 member1316917136on_fml: produc591588199on_fml > set_Pr519625031on_fml > $o ).
% 4.36/2.18
% 4.36/2.18 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Otrm_J_Mt__Option__Ooption_It__Syntax__Otrm_J_J_Mt__Product____Type__Oprod_It__Option__Ooption_It__Syntax__Otrm_J_Mt__Option__Ooption_It__Syntax__Otrm_J_J_J,type,
% 4.36/2.18 member602811152on_trm: produc2024965863on_trm > set_Pr1062384839on_trm > $o ).
% 4.36/2.18
% 4.36/2.18 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Syntax__Otrm_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Syntax__Otrm_J_J,type,
% 4.36/2.18 member1150310282le_trm: produc1279577057le_trm > set_Pr1969262145le_trm > $o ).
% 4.36/2.18
% 4.36/2.18 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_Mt__Product____Type__Oprod_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J_J,type,
% 4.36/2.18 member1950256170on_trm: produc2018724225on_trm > set_Pr1481565921on_trm > $o ).
% 4.36/2.18
% 4.36/2.18 thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Set__Oset_It__Syntax__Ovariable_J_J,type,
% 4.36/2.18 member1978718144riable: produc432717079riable > set_Pr181266295riable > $o ).
% 4.36/2.18
% 4.36/2.18 thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Syntax__Ovariable_J_Mt__Syntax__Otrm_J,type,
% 4.36/2.18 member2122665623le_trm: produc1367888000le_trm > set_Pr1235432374le_trm > $o ).
% 4.36/2.18
% 4.36/2.18 thf(sy_c_member_001t__Product____Type__Oprod_It__String__Ochar_Mt__Option__Ooption_It__Syntax__Otrm_J_J,type,
% 4.36/2.18 member694524327on_trm: produc464795408on_trm > set_Pr943832262on_trm > $o ).
% 4.36/2.18
% 4.36/2.18 thf(sy_c_member_001t__Product____Type__Oprod_It__String__Ochar_Mt__String__Ochar_J,type,
% 4.36/2.18 member1866856748r_char: produc1593312387r_char > set_Pr604539619r_char > $o ).
% 4.36/2.18
% 4.36/2.18 thf(sy_c_member_001t__Product____Type__Oprod_It__Syntax__Otrm_Mt__Syntax__Otrm_J,type,
% 4.36/2.18 member1735386832rm_trm: product_prod_trm_trm > set_Pr491793543rm_trm > $o ).
% 4.36/2.18
% 4.36/2.18 thf(sy_c_member_001t__String__Ochar,type,
% 4.36/2.18 member_char: char > set_char > $o ).
% 4.36/2.18
% 4.36/2.18 thf(sy_c_member_001t__Syntax__Ovariable,type,
% 4.36/2.18 member_variable: variable > set_variable > $o ).
% 4.36/2.18
% 4.36/2.18 thf(sy_v_U,type,
% 4.36/2.18 u: set_variable ).
% 4.36/2.18
% 4.36/2.18 thf(sy_v_Ua____,type,
% 4.36/2.18 ua: set_variable ).
% 4.36/2.18
% 4.36/2.18 thf(sy_v__092_060eta_062____,type,
% 4.36/2.18 eta: trm ).
% 4.36/2.18
% 4.36/2.18 thf(sy_v__092_060nu_062,type,
% 4.36/2.18 nu: variable > real ).
% 4.36/2.18
% 4.36/2.18 thf(sy_v__092_060nu_062_H____,type,
% 4.36/2.18 nu2: variable > real ).
% 4.36/2.18
% 4.36/2.18 thf(sy_v__092_060omega_062,type,
% 4.36/2.18 omega: variable > real ).
% 4.36/2.18
% 4.36/2.18 thf(sy_v__092_060omega_062_H____,type,
% 4.36/2.18 omega2: variable > real ).
% 4.36/2.18
% 4.36/2.18 thf(sy_v__092_060sigma_062_H_H____,type,
% 4.36/2.18 sigma: produc1418842292n_game ).
% 4.36/2.18
% 4.36/2.18 thf(sy_v__092_060theta_062____,type,
% 4.36/2.18 theta: trm ).
% 4.36/2.18
% 4.36/2.18 thf(fact_0_vaouter,axiom,
% 4.36/2.18 denota1419872369iation @ nu @ omega @ u ).
% 4.36/2.18
% 4.36/2.18 thf(fact_1_usubstappf__geq__conv,axiom,
% 4.36/2.18 ! [Sigma: produc1418842292n_game,U: set_variable,Theta: trm,Eta: trm] :
% 4.36/2.18 ( ( ( uSubst516392804stappf @ Sigma @ U @ ( geq @ Theta @ Eta ) )
% 4.36/2.18 != none_fml )
% 4.36/2.18 => ( ( ( uSubst516392818stappt @ Sigma @ U @ Theta )
% 4.36/2.18 != none_trm )
% 4.36/2.18 & ( ( uSubst516392818stappt @ Sigma @ U @ Eta )
% 4.36/2.18 != none_trm ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_2_Geq_Oprems_I1_J,axiom,
% 4.36/2.18 ( ( uSubst516392804stappf @ sigma @ ua @ ( geq @ theta @ eta ) )
% 4.36/2.18 != none_fml ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_3_undeft__None,axiom,
% 4.36/2.18 none_trm = none_trm ).
% 4.36/2.18
% 4.36/2.18 thf(fact_4_usubstappt__det,axiom,
% 4.36/2.18 ! [Sigma: produc1418842292n_game,U: set_variable,Theta: trm,V: set_variable] :
% 4.36/2.18 ( ( ( uSubst516392818stappt @ Sigma @ U @ Theta )
% 4.36/2.18 != none_trm )
% 4.36/2.18 => ( ( ( uSubst516392818stappt @ Sigma @ V @ Theta )
% 4.36/2.18 != none_trm )
% 4.36/2.18 => ( ( uSubst516392818stappt @ Sigma @ U @ Theta )
% 4.36/2.18 = ( uSubst516392818stappt @ Sigma @ V @ Theta ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_5_Geq_Oprems_I2_J,axiom,
% 4.36/2.18 denota1419872369iation @ nu2 @ omega2 @ ua ).
% 4.36/2.18
% 4.36/2.18 thf(fact_6_usubstappt__plus__conv,axiom,
% 4.36/2.18 ! [Sigma: produc1418842292n_game,U: set_variable,Theta: trm,Eta: trm] :
% 4.36/2.18 ( ( ( uSubst516392818stappt @ Sigma @ U @ ( plus @ Theta @ Eta ) )
% 4.36/2.18 != none_trm )
% 4.36/2.18 => ( ( ( uSubst516392818stappt @ Sigma @ U @ Theta )
% 4.36/2.18 != none_trm )
% 4.36/2.18 & ( ( uSubst516392818stappt @ Sigma @ U @ Eta )
% 4.36/2.18 != none_trm ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_7_usubstappt__times__conv,axiom,
% 4.36/2.18 ! [Sigma: produc1418842292n_game,U: set_variable,Theta: trm,Eta: trm] :
% 4.36/2.18 ( ( ( uSubst516392818stappt @ Sigma @ U @ ( times @ Theta @ Eta ) )
% 4.36/2.18 != none_trm )
% 4.36/2.18 => ( ( ( uSubst516392818stappt @ Sigma @ U @ Theta )
% 4.36/2.18 != none_trm )
% 4.36/2.18 & ( ( uSubst516392818stappt @ Sigma @ U @ Eta )
% 4.36/2.18 != none_trm ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_8_usubstappt__antimon,axiom,
% 4.36/2.18 ! [V: set_variable,U: set_variable,Sigma: produc1418842292n_game,Theta: trm] :
% 4.36/2.18 ( ( ord_le282106107riable @ V @ U )
% 4.36/2.18 => ( ( ( uSubst516392818stappt @ Sigma @ U @ Theta )
% 4.36/2.18 != none_trm )
% 4.36/2.18 => ( ( uSubst516392818stappt @ Sigma @ U @ Theta )
% 4.36/2.18 = ( uSubst516392818stappt @ Sigma @ V @ Theta ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_9_Differentialo_Osimps_I2_J,axiom,
% 4.36/2.18 ( ( uSubst716837505ntialo @ none_trm )
% 4.36/2.18 = none_trm ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_10_Differentialo__undef,axiom,
% 4.36/2.18 ! [Theta: option_trm] :
% 4.36/2.18 ( ( ( uSubst716837505ntialo @ Theta )
% 4.36/2.18 = none_trm )
% 4.36/2.18 = ( Theta = none_trm ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_11_Pluso_Osimps_I2_J,axiom,
% 4.36/2.18 ! [Eta: option_trm] :
% 4.36/2.18 ( ( uSubst141955042_Pluso @ none_trm @ Eta )
% 4.36/2.18 = none_trm ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_12_Timeso_Osimps_I2_J,axiom,
% 4.36/2.18 ! [Eta: option_trm] :
% 4.36/2.18 ( ( uSubst918876924Timeso @ none_trm @ Eta )
% 4.36/2.18 = none_trm ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_13_Pluso__undef,axiom,
% 4.36/2.18 ! [Theta: option_trm,Eta: option_trm] :
% 4.36/2.18 ( ( ( uSubst141955042_Pluso @ Theta @ Eta )
% 4.36/2.18 = none_trm )
% 4.36/2.18 = ( ( Theta = none_trm )
% 4.36/2.18 | ( Eta = none_trm ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_14_Timeso__undef,axiom,
% 4.36/2.18 ! [Theta: option_trm,Eta: option_trm] :
% 4.36/2.18 ( ( ( uSubst918876924Timeso @ Theta @ Eta )
% 4.36/2.18 = none_trm )
% 4.36/2.18 = ( ( Theta = none_trm )
% 4.36/2.18 | ( Eta = none_trm ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_15_Geqo_Osimps_I2_J,axiom,
% 4.36/2.18 ! [Eta: option_trm] :
% 4.36/2.18 ( ( uSubst152838031e_Geqo @ none_trm @ Eta )
% 4.36/2.18 = none_fml ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_16_usubstappf__antimon,axiom,
% 4.36/2.18 ! [V: set_variable,U: set_variable,Sigma: produc1418842292n_game,Phi: fml] :
% 4.36/2.18 ( ( ord_le282106107riable @ V @ U )
% 4.36/2.18 => ( ( ( uSubst516392804stappf @ Sigma @ U @ Phi )
% 4.36/2.18 != none_fml )
% 4.36/2.18 => ( ( uSubst516392804stappf @ Sigma @ U @ Phi )
% 4.36/2.18 = ( uSubst516392804stappf @ Sigma @ V @ Phi ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_17_usubstappf__det,axiom,
% 4.36/2.18 ! [Sigma: produc1418842292n_game,U: set_variable,Phi: fml,V: set_variable] :
% 4.36/2.18 ( ( ( uSubst516392804stappf @ Sigma @ U @ Phi )
% 4.36/2.18 != none_fml )
% 4.36/2.18 => ( ( ( uSubst516392804stappf @ Sigma @ V @ Phi )
% 4.36/2.18 != none_fml )
% 4.36/2.18 => ( ( uSubst516392804stappf @ Sigma @ U @ Phi )
% 4.36/2.18 = ( uSubst516392804stappf @ Sigma @ V @ Phi ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_18_usubstappt_Osimps_I5_J,axiom,
% 4.36/2.18 ! [Sigma: produc1418842292n_game,U: set_variable,Theta: trm,Eta: trm] :
% 4.36/2.18 ( ( uSubst516392818stappt @ Sigma @ U @ ( plus @ Theta @ Eta ) )
% 4.36/2.18 = ( uSubst141955042_Pluso @ ( uSubst516392818stappt @ Sigma @ U @ Theta ) @ ( uSubst516392818stappt @ Sigma @ U @ Eta ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_19_usubstappt_Osimps_I6_J,axiom,
% 4.36/2.18 ! [Sigma: produc1418842292n_game,U: set_variable,Theta: trm,Eta: trm] :
% 4.36/2.18 ( ( uSubst516392818stappt @ Sigma @ U @ ( times @ Theta @ Eta ) )
% 4.36/2.18 = ( uSubst918876924Timeso @ ( uSubst516392818stappt @ Sigma @ U @ Theta ) @ ( uSubst516392818stappt @ Sigma @ U @ Eta ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_20_usubstappf_Osimps_I2_J,axiom,
% 4.36/2.18 ! [Sigma: produc1418842292n_game,U: set_variable,Theta: trm,Eta: trm] :
% 4.36/2.18 ( ( uSubst516392804stappf @ Sigma @ U @ ( geq @ Theta @ Eta ) )
% 4.36/2.18 = ( uSubst152838031e_Geqo @ ( uSubst516392818stappt @ Sigma @ U @ Theta ) @ ( uSubst516392818stappt @ Sigma @ U @ Eta ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_21_Geqo__undef,axiom,
% 4.36/2.18 ! [Theta: option_trm,Eta: option_trm] :
% 4.36/2.18 ( ( ( uSubst152838031e_Geqo @ Theta @ Eta )
% 4.36/2.18 = none_fml )
% 4.36/2.18 = ( ( Theta = none_trm )
% 4.36/2.18 | ( Eta = none_trm ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_22_trm_Oinject_I6_J,axiom,
% 4.36/2.18 ! [X61: trm,X62: trm,Y61: trm,Y62: trm] :
% 4.36/2.18 ( ( ( times @ X61 @ X62 )
% 4.36/2.18 = ( times @ Y61 @ Y62 ) )
% 4.36/2.18 = ( ( X61 = Y61 )
% 4.36/2.18 & ( X62 = Y62 ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_23_trm_Oinject_I5_J,axiom,
% 4.36/2.18 ! [X51: trm,X52: trm,Y51: trm,Y52: trm] :
% 4.36/2.18 ( ( ( plus @ X51 @ X52 )
% 4.36/2.18 = ( plus @ Y51 @ Y52 ) )
% 4.36/2.18 = ( ( X51 = Y51 )
% 4.36/2.18 & ( X52 = Y52 ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_24_fml_Oinject_I2_J,axiom,
% 4.36/2.18 ! [X21: trm,X22: trm,Y21: trm,Y22: trm] :
% 4.36/2.18 ( ( ( geq @ X21 @ X22 )
% 4.36/2.18 = ( geq @ Y21 @ Y22 ) )
% 4.36/2.18 = ( ( X21 = Y21 )
% 4.36/2.18 & ( X22 = Y22 ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_25_Uvariation__mon,axiom,
% 4.36/2.18 ! [U: set_variable,V: set_variable,Omega: variable > real,Nu: variable > real] :
% 4.36/2.18 ( ( ord_le282106107riable @ U @ V )
% 4.36/2.18 => ( ( denota1419872369iation @ Omega @ Nu @ U )
% 4.36/2.18 => ( denota1419872369iation @ Omega @ Nu @ V ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_26_subsetI,axiom,
% 4.36/2.18 ! [A: set_char,B: set_char] :
% 4.36/2.18 ( ! [X: char] :
% 4.36/2.18 ( ( member_char @ X @ A )
% 4.36/2.18 => ( member_char @ X @ B ) )
% 4.36/2.18 => ( ord_less_eq_set_char @ A @ B ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_27_subsetI,axiom,
% 4.36/2.18 ! [A: set_variable,B: set_variable] :
% 4.36/2.18 ( ! [X: variable] :
% 4.36/2.18 ( ( member_variable @ X @ A )
% 4.36/2.18 => ( member_variable @ X @ B ) )
% 4.36/2.18 => ( ord_le282106107riable @ A @ B ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_28_subset__antisym,axiom,
% 4.36/2.18 ! [A: set_variable,B: set_variable] :
% 4.36/2.18 ( ( ord_le282106107riable @ A @ B )
% 4.36/2.18 => ( ( ord_le282106107riable @ B @ A )
% 4.36/2.18 => ( A = B ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_29_trm_Odistinct_I37_J,axiom,
% 4.36/2.18 ! [X51: trm,X52: trm,X61: trm,X62: trm] :
% 4.36/2.18 ( ( plus @ X51 @ X52 )
% 4.36/2.18 != ( times @ X61 @ X62 ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_30_order__refl,axiom,
% 4.36/2.18 ! [X2: set_variable] : ( ord_le282106107riable @ X2 @ X2 ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_31_Uvariation__univ,axiom,
% 4.36/2.18 ! [Nu: variable > real,Nu2: variable > real] :
% 4.36/2.18 ( denota1419872369iation @ Nu @ Nu2
% 4.36/2.18 @ ( collect_variable
% 4.36/2.18 @ ^ [X3: variable] : $true ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_32_Collect__subset,axiom,
% 4.36/2.18 ! [A: set_char,P: char > $o] :
% 4.36/2.18 ( ord_less_eq_set_char
% 4.36/2.18 @ ( collect_char
% 4.36/2.18 @ ^ [X3: char] :
% 4.36/2.18 ( ( member_char @ X3 @ A )
% 4.36/2.18 & ( P @ X3 ) ) )
% 4.36/2.18 @ A ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_33_Collect__subset,axiom,
% 4.36/2.18 ! [A: set_variable,P: variable > $o] :
% 4.36/2.18 ( ord_le282106107riable
% 4.36/2.18 @ ( collect_variable
% 4.36/2.18 @ ^ [X3: variable] :
% 4.36/2.18 ( ( member_variable @ X3 @ A )
% 4.36/2.18 & ( P @ X3 ) ) )
% 4.36/2.18 @ A ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_34_less__eq__set__def,axiom,
% 4.36/2.18 ( ord_less_eq_set_char
% 4.36/2.18 = ( ^ [A2: set_char,B2: set_char] :
% 4.36/2.18 ( ord_less_eq_char_o
% 4.36/2.18 @ ^ [X3: char] : ( member_char @ X3 @ A2 )
% 4.36/2.18 @ ^ [X3: char] : ( member_char @ X3 @ B2 ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_35_less__eq__set__def,axiom,
% 4.36/2.18 ( ord_le282106107riable
% 4.36/2.18 = ( ^ [A2: set_variable,B2: set_variable] :
% 4.36/2.18 ( ord_le1407353162able_o
% 4.36/2.18 @ ^ [X3: variable] : ( member_variable @ X3 @ A2 )
% 4.36/2.18 @ ^ [X3: variable] : ( member_variable @ X3 @ B2 ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_36_dual__order_Oantisym,axiom,
% 4.36/2.18 ! [B3: set_variable,A3: set_variable] :
% 4.36/2.18 ( ( ord_le282106107riable @ B3 @ A3 )
% 4.36/2.18 => ( ( ord_le282106107riable @ A3 @ B3 )
% 4.36/2.18 => ( A3 = B3 ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_37_dual__order_Oeq__iff,axiom,
% 4.36/2.18 ( ( ^ [Y: set_variable,Z: set_variable] : ( Y = Z ) )
% 4.36/2.18 = ( ^ [A4: set_variable,B4: set_variable] :
% 4.36/2.18 ( ( ord_le282106107riable @ B4 @ A4 )
% 4.36/2.18 & ( ord_le282106107riable @ A4 @ B4 ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_38_dual__order_Otrans,axiom,
% 4.36/2.18 ! [B3: set_variable,A3: set_variable,C: set_variable] :
% 4.36/2.18 ( ( ord_le282106107riable @ B3 @ A3 )
% 4.36/2.18 => ( ( ord_le282106107riable @ C @ B3 )
% 4.36/2.18 => ( ord_le282106107riable @ C @ A3 ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_39_dual__order_Orefl,axiom,
% 4.36/2.18 ! [A3: set_variable] : ( ord_le282106107riable @ A3 @ A3 ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_40_order__trans,axiom,
% 4.36/2.18 ! [X2: set_variable,Y2: set_variable,Z2: set_variable] :
% 4.36/2.18 ( ( ord_le282106107riable @ X2 @ Y2 )
% 4.36/2.18 => ( ( ord_le282106107riable @ Y2 @ Z2 )
% 4.36/2.18 => ( ord_le282106107riable @ X2 @ Z2 ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_41_order__class_Oorder_Oantisym,axiom,
% 4.36/2.18 ! [A3: set_variable,B3: set_variable] :
% 4.36/2.18 ( ( ord_le282106107riable @ A3 @ B3 )
% 4.36/2.18 => ( ( ord_le282106107riable @ B3 @ A3 )
% 4.36/2.18 => ( A3 = B3 ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_42_ord__le__eq__trans,axiom,
% 4.36/2.18 ! [A3: set_variable,B3: set_variable,C: set_variable] :
% 4.36/2.18 ( ( ord_le282106107riable @ A3 @ B3 )
% 4.36/2.18 => ( ( B3 = C )
% 4.36/2.18 => ( ord_le282106107riable @ A3 @ C ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_43_ord__eq__le__trans,axiom,
% 4.36/2.18 ! [A3: set_variable,B3: set_variable,C: set_variable] :
% 4.36/2.18 ( ( A3 = B3 )
% 4.36/2.18 => ( ( ord_le282106107riable @ B3 @ C )
% 4.36/2.18 => ( ord_le282106107riable @ A3 @ C ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_44_order__class_Oorder_Oeq__iff,axiom,
% 4.36/2.18 ( ( ^ [Y: set_variable,Z: set_variable] : ( Y = Z ) )
% 4.36/2.18 = ( ^ [A4: set_variable,B4: set_variable] :
% 4.36/2.18 ( ( ord_le282106107riable @ A4 @ B4 )
% 4.36/2.18 & ( ord_le282106107riable @ B4 @ A4 ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_45_antisym__conv,axiom,
% 4.36/2.18 ! [Y2: set_variable,X2: set_variable] :
% 4.36/2.18 ( ( ord_le282106107riable @ Y2 @ X2 )
% 4.36/2.18 => ( ( ord_le282106107riable @ X2 @ Y2 )
% 4.36/2.18 = ( X2 = Y2 ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_46_mem__Collect__eq,axiom,
% 4.36/2.18 ! [A3: variable,P: variable > $o] :
% 4.36/2.18 ( ( member_variable @ A3 @ ( collect_variable @ P ) )
% 4.36/2.18 = ( P @ A3 ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_47_mem__Collect__eq,axiom,
% 4.36/2.18 ! [A3: char,P: char > $o] :
% 4.36/2.18 ( ( member_char @ A3 @ ( collect_char @ P ) )
% 4.36/2.18 = ( P @ A3 ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_48_Collect__mem__eq,axiom,
% 4.36/2.18 ! [A: set_variable] :
% 4.36/2.18 ( ( collect_variable
% 4.36/2.18 @ ^ [X3: variable] : ( member_variable @ X3 @ A ) )
% 4.36/2.18 = A ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_49_Collect__mem__eq,axiom,
% 4.36/2.18 ! [A: set_char] :
% 4.36/2.18 ( ( collect_char
% 4.36/2.18 @ ^ [X3: char] : ( member_char @ X3 @ A ) )
% 4.36/2.18 = A ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_50_Collect__cong,axiom,
% 4.36/2.18 ! [P: variable > $o,Q: variable > $o] :
% 4.36/2.18 ( ! [X: variable] :
% 4.36/2.18 ( ( P @ X )
% 4.36/2.18 = ( Q @ X ) )
% 4.36/2.18 => ( ( collect_variable @ P )
% 4.36/2.18 = ( collect_variable @ Q ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_51_Collect__cong,axiom,
% 4.36/2.18 ! [P: char > $o,Q: char > $o] :
% 4.36/2.18 ( ! [X: char] :
% 4.36/2.18 ( ( P @ X )
% 4.36/2.18 = ( Q @ X ) )
% 4.36/2.18 => ( ( collect_char @ P )
% 4.36/2.18 = ( collect_char @ Q ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_52_order_Otrans,axiom,
% 4.36/2.18 ! [A3: set_variable,B3: set_variable,C: set_variable] :
% 4.36/2.18 ( ( ord_le282106107riable @ A3 @ B3 )
% 4.36/2.18 => ( ( ord_le282106107riable @ B3 @ C )
% 4.36/2.18 => ( ord_le282106107riable @ A3 @ C ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_53_eq__refl,axiom,
% 4.36/2.18 ! [X2: set_variable,Y2: set_variable] :
% 4.36/2.18 ( ( X2 = Y2 )
% 4.36/2.18 => ( ord_le282106107riable @ X2 @ Y2 ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_54_antisym,axiom,
% 4.36/2.18 ! [X2: set_variable,Y2: set_variable] :
% 4.36/2.18 ( ( ord_le282106107riable @ X2 @ Y2 )
% 4.36/2.18 => ( ( ord_le282106107riable @ Y2 @ X2 )
% 4.36/2.18 => ( X2 = Y2 ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_55_eq__iff,axiom,
% 4.36/2.18 ( ( ^ [Y: set_variable,Z: set_variable] : ( Y = Z ) )
% 4.36/2.18 = ( ^ [X3: set_variable,Y3: set_variable] :
% 4.36/2.18 ( ( ord_le282106107riable @ X3 @ Y3 )
% 4.36/2.18 & ( ord_le282106107riable @ Y3 @ X3 ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_56_ord__le__eq__subst,axiom,
% 4.36/2.18 ! [A3: set_variable,B3: set_variable,F: set_variable > set_variable,C: set_variable] :
% 4.36/2.18 ( ( ord_le282106107riable @ A3 @ B3 )
% 4.36/2.18 => ( ( ( F @ B3 )
% 4.36/2.18 = C )
% 4.36/2.18 => ( ! [X: set_variable,Y4: set_variable] :
% 4.36/2.18 ( ( ord_le282106107riable @ X @ Y4 )
% 4.36/2.18 => ( ord_le282106107riable @ ( F @ X ) @ ( F @ Y4 ) ) )
% 4.36/2.18 => ( ord_le282106107riable @ ( F @ A3 ) @ C ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_57_ord__eq__le__subst,axiom,
% 4.36/2.18 ! [A3: set_variable,F: set_variable > set_variable,B3: set_variable,C: set_variable] :
% 4.36/2.18 ( ( A3
% 4.36/2.18 = ( F @ B3 ) )
% 4.36/2.18 => ( ( ord_le282106107riable @ B3 @ C )
% 4.36/2.18 => ( ! [X: set_variable,Y4: set_variable] :
% 4.36/2.18 ( ( ord_le282106107riable @ X @ Y4 )
% 4.36/2.18 => ( ord_le282106107riable @ ( F @ X ) @ ( F @ Y4 ) ) )
% 4.36/2.18 => ( ord_le282106107riable @ A3 @ ( F @ C ) ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_58_order__subst2,axiom,
% 4.36/2.18 ! [A3: set_variable,B3: set_variable,F: set_variable > set_variable,C: set_variable] :
% 4.36/2.18 ( ( ord_le282106107riable @ A3 @ B3 )
% 4.36/2.18 => ( ( ord_le282106107riable @ ( F @ B3 ) @ C )
% 4.36/2.18 => ( ! [X: set_variable,Y4: set_variable] :
% 4.36/2.18 ( ( ord_le282106107riable @ X @ Y4 )
% 4.36/2.18 => ( ord_le282106107riable @ ( F @ X ) @ ( F @ Y4 ) ) )
% 4.36/2.18 => ( ord_le282106107riable @ ( F @ A3 ) @ C ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_59_order__subst1,axiom,
% 4.36/2.18 ! [A3: set_variable,F: set_variable > set_variable,B3: set_variable,C: set_variable] :
% 4.36/2.18 ( ( ord_le282106107riable @ A3 @ ( F @ B3 ) )
% 4.36/2.18 => ( ( ord_le282106107riable @ B3 @ C )
% 4.36/2.18 => ( ! [X: set_variable,Y4: set_variable] :
% 4.36/2.18 ( ( ord_le282106107riable @ X @ Y4 )
% 4.36/2.18 => ( ord_le282106107riable @ ( F @ X ) @ ( F @ Y4 ) ) )
% 4.36/2.18 => ( ord_le282106107riable @ A3 @ ( F @ C ) ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_60_Collect__mono__iff,axiom,
% 4.36/2.18 ! [P: char > $o,Q: char > $o] :
% 4.36/2.18 ( ( ord_less_eq_set_char @ ( collect_char @ P ) @ ( collect_char @ Q ) )
% 4.36/2.18 = ( ! [X3: char] :
% 4.36/2.18 ( ( P @ X3 )
% 4.36/2.18 => ( Q @ X3 ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_61_Collect__mono__iff,axiom,
% 4.36/2.18 ! [P: variable > $o,Q: variable > $o] :
% 4.36/2.18 ( ( ord_le282106107riable @ ( collect_variable @ P ) @ ( collect_variable @ Q ) )
% 4.36/2.18 = ( ! [X3: variable] :
% 4.36/2.18 ( ( P @ X3 )
% 4.36/2.18 => ( Q @ X3 ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_62_set__eq__subset,axiom,
% 4.36/2.18 ( ( ^ [Y: set_variable,Z: set_variable] : ( Y = Z ) )
% 4.36/2.18 = ( ^ [A2: set_variable,B2: set_variable] :
% 4.36/2.18 ( ( ord_le282106107riable @ A2 @ B2 )
% 4.36/2.18 & ( ord_le282106107riable @ B2 @ A2 ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_63_subset__trans,axiom,
% 4.36/2.18 ! [A: set_variable,B: set_variable,C2: set_variable] :
% 4.36/2.18 ( ( ord_le282106107riable @ A @ B )
% 4.36/2.18 => ( ( ord_le282106107riable @ B @ C2 )
% 4.36/2.18 => ( ord_le282106107riable @ A @ C2 ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_64_Collect__mono,axiom,
% 4.36/2.18 ! [P: char > $o,Q: char > $o] :
% 4.36/2.18 ( ! [X: char] :
% 4.36/2.18 ( ( P @ X )
% 4.36/2.18 => ( Q @ X ) )
% 4.36/2.18 => ( ord_less_eq_set_char @ ( collect_char @ P ) @ ( collect_char @ Q ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_65_Collect__mono,axiom,
% 4.36/2.18 ! [P: variable > $o,Q: variable > $o] :
% 4.36/2.18 ( ! [X: variable] :
% 4.36/2.18 ( ( P @ X )
% 4.36/2.18 => ( Q @ X ) )
% 4.36/2.18 => ( ord_le282106107riable @ ( collect_variable @ P ) @ ( collect_variable @ Q ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_66_subset__refl,axiom,
% 4.36/2.18 ! [A: set_variable] : ( ord_le282106107riable @ A @ A ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_67_subset__iff,axiom,
% 4.36/2.18 ( ord_less_eq_set_char
% 4.36/2.18 = ( ^ [A2: set_char,B2: set_char] :
% 4.36/2.18 ! [T: char] :
% 4.36/2.18 ( ( member_char @ T @ A2 )
% 4.36/2.18 => ( member_char @ T @ B2 ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_68_subset__iff,axiom,
% 4.36/2.18 ( ord_le282106107riable
% 4.36/2.18 = ( ^ [A2: set_variable,B2: set_variable] :
% 4.36/2.18 ! [T: variable] :
% 4.36/2.18 ( ( member_variable @ T @ A2 )
% 4.36/2.18 => ( member_variable @ T @ B2 ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_69_equalityD2,axiom,
% 4.36/2.18 ! [A: set_variable,B: set_variable] :
% 4.36/2.18 ( ( A = B )
% 4.36/2.18 => ( ord_le282106107riable @ B @ A ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_70_equalityD1,axiom,
% 4.36/2.18 ! [A: set_variable,B: set_variable] :
% 4.36/2.18 ( ( A = B )
% 4.36/2.18 => ( ord_le282106107riable @ A @ B ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_71_subset__eq,axiom,
% 4.36/2.18 ( ord_less_eq_set_char
% 4.36/2.18 = ( ^ [A2: set_char,B2: set_char] :
% 4.36/2.18 ! [X3: char] :
% 4.36/2.18 ( ( member_char @ X3 @ A2 )
% 4.36/2.18 => ( member_char @ X3 @ B2 ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_72_subset__eq,axiom,
% 4.36/2.18 ( ord_le282106107riable
% 4.36/2.18 = ( ^ [A2: set_variable,B2: set_variable] :
% 4.36/2.18 ! [X3: variable] :
% 4.36/2.18 ( ( member_variable @ X3 @ A2 )
% 4.36/2.18 => ( member_variable @ X3 @ B2 ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_73_equalityE,axiom,
% 4.36/2.18 ! [A: set_variable,B: set_variable] :
% 4.36/2.18 ( ( A = B )
% 4.36/2.18 => ~ ( ( ord_le282106107riable @ A @ B )
% 4.36/2.18 => ~ ( ord_le282106107riable @ B @ A ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_74_subsetD,axiom,
% 4.36/2.18 ! [A: set_char,B: set_char,C: char] :
% 4.36/2.18 ( ( ord_less_eq_set_char @ A @ B )
% 4.36/2.18 => ( ( member_char @ C @ A )
% 4.36/2.18 => ( member_char @ C @ B ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_75_subsetD,axiom,
% 4.36/2.18 ! [A: set_variable,B: set_variable,C: variable] :
% 4.36/2.18 ( ( ord_le282106107riable @ A @ B )
% 4.36/2.18 => ( ( member_variable @ C @ A )
% 4.36/2.18 => ( member_variable @ C @ B ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_76_in__mono,axiom,
% 4.36/2.18 ! [A: set_char,B: set_char,X2: char] :
% 4.36/2.18 ( ( ord_less_eq_set_char @ A @ B )
% 4.36/2.18 => ( ( member_char @ X2 @ A )
% 4.36/2.18 => ( member_char @ X2 @ B ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_77_in__mono,axiom,
% 4.36/2.18 ! [A: set_variable,B: set_variable,X2: variable] :
% 4.36/2.18 ( ( ord_le282106107riable @ A @ B )
% 4.36/2.18 => ( ( member_variable @ X2 @ A )
% 4.36/2.18 => ( member_variable @ X2 @ B ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_78_Uvariation__sym__rel,axiom,
% 4.36/2.18 ! [Omega: variable > real,Nu: variable > real,U: set_variable] :
% 4.36/2.18 ( ( denota1419872369iation @ Omega @ Nu @ U )
% 4.36/2.18 => ( denota1419872369iation @ Nu @ Omega @ U ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_79_Uvariation__refl,axiom,
% 4.36/2.18 ! [Nu: variable > real,V: set_variable] : ( denota1419872369iation @ Nu @ Nu @ V ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_80_Uvariation__sym,axiom,
% 4.36/2.18 ( denota1419872369iation
% 4.36/2.18 = ( ^ [Omega2: variable > real,Nu3: variable > real] : ( denota1419872369iation @ Nu3 @ Omega2 ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_81_Uvariation__def,axiom,
% 4.36/2.18 ( denota1419872369iation
% 4.36/2.18 = ( ^ [Nu3: variable > real,Nu4: variable > real,U2: set_variable] :
% 4.36/2.18 ! [I: variable] :
% 4.36/2.18 ( ~ ( member_variable @ I @ U2 )
% 4.36/2.18 => ( ( Nu3 @ I )
% 4.36/2.18 = ( Nu4 @ I ) ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_82_pred__subset__eq,axiom,
% 4.36/2.18 ! [R: set_char,S: set_char] :
% 4.36/2.18 ( ( ord_less_eq_char_o
% 4.36/2.18 @ ^ [X3: char] : ( member_char @ X3 @ R )
% 4.36/2.18 @ ^ [X3: char] : ( member_char @ X3 @ S ) )
% 4.36/2.18 = ( ord_less_eq_set_char @ R @ S ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_83_pred__subset__eq,axiom,
% 4.36/2.18 ! [R: set_variable,S: set_variable] :
% 4.36/2.18 ( ( ord_le1407353162able_o
% 4.36/2.18 @ ^ [X3: variable] : ( member_variable @ X3 @ R )
% 4.36/2.18 @ ^ [X3: variable] : ( member_variable @ X3 @ S ) )
% 4.36/2.18 = ( ord_le282106107riable @ R @ S ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_84_subset__Collect__iff,axiom,
% 4.36/2.18 ! [B: set_char,A: set_char,P: char > $o] :
% 4.36/2.18 ( ( ord_less_eq_set_char @ B @ A )
% 4.36/2.18 => ( ( ord_less_eq_set_char @ B
% 4.36/2.18 @ ( collect_char
% 4.36/2.18 @ ^ [X3: char] :
% 4.36/2.18 ( ( member_char @ X3 @ A )
% 4.36/2.18 & ( P @ X3 ) ) ) )
% 4.36/2.18 = ( ! [X3: char] :
% 4.36/2.18 ( ( member_char @ X3 @ B )
% 4.36/2.18 => ( P @ X3 ) ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_85_subset__Collect__iff,axiom,
% 4.36/2.18 ! [B: set_variable,A: set_variable,P: variable > $o] :
% 4.36/2.18 ( ( ord_le282106107riable @ B @ A )
% 4.36/2.18 => ( ( ord_le282106107riable @ B
% 4.36/2.18 @ ( collect_variable
% 4.36/2.18 @ ^ [X3: variable] :
% 4.36/2.18 ( ( member_variable @ X3 @ A )
% 4.36/2.18 & ( P @ X3 ) ) ) )
% 4.36/2.18 = ( ! [X3: variable] :
% 4.36/2.18 ( ( member_variable @ X3 @ B )
% 4.36/2.18 => ( P @ X3 ) ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_86_subset__CollectI,axiom,
% 4.36/2.18 ! [B: set_char,A: set_char,Q: char > $o,P: char > $o] :
% 4.36/2.18 ( ( ord_less_eq_set_char @ B @ A )
% 4.36/2.18 => ( ! [X: char] :
% 4.36/2.18 ( ( member_char @ X @ B )
% 4.36/2.18 => ( ( Q @ X )
% 4.36/2.18 => ( P @ X ) ) )
% 4.36/2.18 => ( ord_less_eq_set_char
% 4.36/2.18 @ ( collect_char
% 4.36/2.18 @ ^ [X3: char] :
% 4.36/2.18 ( ( member_char @ X3 @ B )
% 4.36/2.18 & ( Q @ X3 ) ) )
% 4.36/2.18 @ ( collect_char
% 4.36/2.18 @ ^ [X3: char] :
% 4.36/2.18 ( ( member_char @ X3 @ A )
% 4.36/2.18 & ( P @ X3 ) ) ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_87_subset__CollectI,axiom,
% 4.36/2.18 ! [B: set_variable,A: set_variable,Q: variable > $o,P: variable > $o] :
% 4.36/2.18 ( ( ord_le282106107riable @ B @ A )
% 4.36/2.18 => ( ! [X: variable] :
% 4.36/2.18 ( ( member_variable @ X @ B )
% 4.36/2.18 => ( ( Q @ X )
% 4.36/2.18 => ( P @ X ) ) )
% 4.36/2.18 => ( ord_le282106107riable
% 4.36/2.18 @ ( collect_variable
% 4.36/2.18 @ ^ [X3: variable] :
% 4.36/2.18 ( ( member_variable @ X3 @ B )
% 4.36/2.18 & ( Q @ X3 ) ) )
% 4.36/2.18 @ ( collect_variable
% 4.36/2.18 @ ^ [X3: variable] :
% 4.36/2.18 ( ( member_variable @ X3 @ A )
% 4.36/2.18 & ( P @ X3 ) ) ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_88_Collect__restrict,axiom,
% 4.36/2.18 ! [X4: set_char,P: char > $o] :
% 4.36/2.18 ( ord_less_eq_set_char
% 4.36/2.18 @ ( collect_char
% 4.36/2.18 @ ^ [X3: char] :
% 4.36/2.18 ( ( member_char @ X3 @ X4 )
% 4.36/2.18 & ( P @ X3 ) ) )
% 4.36/2.18 @ X4 ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_89_Collect__restrict,axiom,
% 4.36/2.18 ! [X4: set_variable,P: variable > $o] :
% 4.36/2.18 ( ord_le282106107riable
% 4.36/2.18 @ ( collect_variable
% 4.36/2.18 @ ^ [X3: variable] :
% 4.36/2.18 ( ( member_variable @ X3 @ X4 )
% 4.36/2.18 & ( P @ X3 ) ) )
% 4.36/2.18 @ X4 ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_90_prop__restrict,axiom,
% 4.36/2.18 ! [X2: char,Z3: set_char,X4: set_char,P: char > $o] :
% 4.36/2.18 ( ( member_char @ X2 @ Z3 )
% 4.36/2.18 => ( ( ord_less_eq_set_char @ Z3
% 4.36/2.18 @ ( collect_char
% 4.36/2.18 @ ^ [X3: char] :
% 4.36/2.18 ( ( member_char @ X3 @ X4 )
% 4.36/2.18 & ( P @ X3 ) ) ) )
% 4.36/2.18 => ( P @ X2 ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_91_prop__restrict,axiom,
% 4.36/2.18 ! [X2: variable,Z3: set_variable,X4: set_variable,P: variable > $o] :
% 4.36/2.18 ( ( member_variable @ X2 @ Z3 )
% 4.36/2.18 => ( ( ord_le282106107riable @ Z3
% 4.36/2.18 @ ( collect_variable
% 4.36/2.18 @ ^ [X3: variable] :
% 4.36/2.18 ( ( member_variable @ X3 @ X4 )
% 4.36/2.18 & ( P @ X3 ) ) ) )
% 4.36/2.18 => ( P @ X2 ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_92_conj__subset__def,axiom,
% 4.36/2.18 ! [A: set_char,P: char > $o,Q: char > $o] :
% 4.36/2.18 ( ( ord_less_eq_set_char @ A
% 4.36/2.18 @ ( collect_char
% 4.36/2.18 @ ^ [X3: char] :
% 4.36/2.18 ( ( P @ X3 )
% 4.36/2.18 & ( Q @ X3 ) ) ) )
% 4.36/2.18 = ( ( ord_less_eq_set_char @ A @ ( collect_char @ P ) )
% 4.36/2.18 & ( ord_less_eq_set_char @ A @ ( collect_char @ Q ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_93_conj__subset__def,axiom,
% 4.36/2.18 ! [A: set_variable,P: variable > $o,Q: variable > $o] :
% 4.36/2.18 ( ( ord_le282106107riable @ A
% 4.36/2.18 @ ( collect_variable
% 4.36/2.18 @ ^ [X3: variable] :
% 4.36/2.18 ( ( P @ X3 )
% 4.36/2.18 & ( Q @ X3 ) ) ) )
% 4.36/2.18 = ( ( ord_le282106107riable @ A @ ( collect_variable @ P ) )
% 4.36/2.18 & ( ord_le282106107riable @ A @ ( collect_variable @ Q ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_94_Pluso_Oelims,axiom,
% 4.36/2.18 ! [X2: option_trm,Xa: option_trm,Y2: option_trm] :
% 4.36/2.18 ( ( ( uSubst141955042_Pluso @ X2 @ Xa )
% 4.36/2.18 = Y2 )
% 4.36/2.18 => ( ! [Theta2: trm] :
% 4.36/2.18 ( ( X2
% 4.36/2.18 = ( some_trm @ Theta2 ) )
% 4.36/2.18 => ! [Eta2: trm] :
% 4.36/2.18 ( ( Xa
% 4.36/2.18 = ( some_trm @ Eta2 ) )
% 4.36/2.18 => ( Y2
% 4.36/2.18 != ( some_trm @ ( plus @ Theta2 @ Eta2 ) ) ) ) )
% 4.36/2.18 => ( ( ( X2 = none_trm )
% 4.36/2.18 => ( Y2 != none_trm ) )
% 4.36/2.18 => ~ ( ? [V2: trm] :
% 4.36/2.18 ( X2
% 4.36/2.18 = ( some_trm @ V2 ) )
% 4.36/2.18 => ( ( Xa = none_trm )
% 4.36/2.18 => ( Y2 != none_trm ) ) ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_95_Timeso_Oelims,axiom,
% 4.36/2.18 ! [X2: option_trm,Xa: option_trm,Y2: option_trm] :
% 4.36/2.18 ( ( ( uSubst918876924Timeso @ X2 @ Xa )
% 4.36/2.18 = Y2 )
% 4.36/2.18 => ( ! [Theta2: trm] :
% 4.36/2.18 ( ( X2
% 4.36/2.18 = ( some_trm @ Theta2 ) )
% 4.36/2.18 => ! [Eta2: trm] :
% 4.36/2.18 ( ( Xa
% 4.36/2.18 = ( some_trm @ Eta2 ) )
% 4.36/2.18 => ( Y2
% 4.36/2.18 != ( some_trm @ ( times @ Theta2 @ Eta2 ) ) ) ) )
% 4.36/2.18 => ( ( ( X2 = none_trm )
% 4.36/2.18 => ( Y2 != none_trm ) )
% 4.36/2.18 => ~ ( ? [V2: trm] :
% 4.36/2.18 ( X2
% 4.36/2.18 = ( some_trm @ V2 ) )
% 4.36/2.18 => ( ( Xa = none_trm )
% 4.36/2.18 => ( Y2 != none_trm ) ) ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_96_usubstappt_Osimps_I7_J,axiom,
% 4.36/2.18 ! [Sigma: produc1418842292n_game,U: set_variable,Theta: trm] :
% 4.36/2.18 ( ( uSubst516392818stappt @ Sigma @ U @ ( differential @ Theta ) )
% 4.36/2.18 = ( uSubst716837505ntialo
% 4.36/2.18 @ ( uSubst516392818stappt @ Sigma
% 4.36/2.18 @ ( collect_variable
% 4.36/2.18 @ ^ [X3: variable] : $true )
% 4.36/2.18 @ Theta ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_97_option_Oinject,axiom,
% 4.36/2.18 ! [X23: trm,Y23: trm] :
% 4.36/2.18 ( ( ( some_trm @ X23 )
% 4.36/2.18 = ( some_trm @ Y23 ) )
% 4.36/2.18 = ( X23 = Y23 ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_98_option_Oinject,axiom,
% 4.36/2.18 ! [X23: fml,Y23: fml] :
% 4.36/2.18 ( ( ( some_fml @ X23 )
% 4.36/2.18 = ( some_fml @ Y23 ) )
% 4.36/2.18 = ( X23 = Y23 ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_99_option_Oinject,axiom,
% 4.36/2.18 ! [X23: game,Y23: game] :
% 4.36/2.18 ( ( ( some_game @ X23 )
% 4.36/2.18 = ( some_game @ Y23 ) )
% 4.36/2.18 = ( X23 = Y23 ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_100_trm_Oinject_I7_J,axiom,
% 4.36/2.18 ! [X7: trm,Y7: trm] :
% 4.36/2.18 ( ( ( differential @ X7 )
% 4.36/2.18 = ( differential @ Y7 ) )
% 4.36/2.18 = ( X7 = Y7 ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_101_not__Some__eq,axiom,
% 4.36/2.18 ! [X2: option_trm] :
% 4.36/2.18 ( ( ! [Y3: trm] :
% 4.36/2.18 ( X2
% 4.36/2.18 != ( some_trm @ Y3 ) ) )
% 4.36/2.18 = ( X2 = none_trm ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_102_not__Some__eq,axiom,
% 4.36/2.18 ! [X2: option_fml] :
% 4.36/2.18 ( ( ! [Y3: fml] :
% 4.36/2.18 ( X2
% 4.36/2.18 != ( some_fml @ Y3 ) ) )
% 4.36/2.18 = ( X2 = none_fml ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_103_not__Some__eq,axiom,
% 4.36/2.18 ! [X2: option_game] :
% 4.36/2.18 ( ( ! [Y3: game] :
% 4.36/2.18 ( X2
% 4.36/2.18 != ( some_game @ Y3 ) ) )
% 4.36/2.18 = ( X2 = none_game ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_104_not__None__eq,axiom,
% 4.36/2.18 ! [X2: option_trm] :
% 4.36/2.18 ( ( X2 != none_trm )
% 4.36/2.18 = ( ? [Y3: trm] :
% 4.36/2.18 ( X2
% 4.36/2.18 = ( some_trm @ Y3 ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_105_not__None__eq,axiom,
% 4.36/2.18 ! [X2: option_fml] :
% 4.36/2.18 ( ( X2 != none_fml )
% 4.36/2.18 = ( ? [Y3: fml] :
% 4.36/2.18 ( X2
% 4.36/2.18 = ( some_fml @ Y3 ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_106_not__None__eq,axiom,
% 4.36/2.18 ! [X2: option_game] :
% 4.36/2.18 ( ( X2 != none_game )
% 4.36/2.18 = ( ? [Y3: game] :
% 4.36/2.18 ( X2
% 4.36/2.18 = ( some_game @ Y3 ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_107_Aterm__Some,axiom,
% 4.36/2.18 some_trm = some_trm ).
% 4.36/2.18
% 4.36/2.18 thf(fact_108_Differentialo_Osimps_I1_J,axiom,
% 4.36/2.18 ! [Theta: trm] :
% 4.36/2.18 ( ( uSubst716837505ntialo @ ( some_trm @ Theta ) )
% 4.36/2.18 = ( some_trm @ ( differential @ Theta ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_109_combine__options__cases,axiom,
% 4.36/2.18 ! [X2: option_trm,P: option_trm > option_trm > $o,Y2: option_trm] :
% 4.36/2.18 ( ( ( X2 = none_trm )
% 4.36/2.18 => ( P @ X2 @ Y2 ) )
% 4.36/2.18 => ( ( ( Y2 = none_trm )
% 4.36/2.18 => ( P @ X2 @ Y2 ) )
% 4.36/2.18 => ( ! [A5: trm,B5: trm] :
% 4.36/2.18 ( ( X2
% 4.36/2.18 = ( some_trm @ A5 ) )
% 4.36/2.18 => ( ( Y2
% 4.36/2.18 = ( some_trm @ B5 ) )
% 4.36/2.18 => ( P @ X2 @ Y2 ) ) )
% 4.36/2.18 => ( P @ X2 @ Y2 ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_110_combine__options__cases,axiom,
% 4.36/2.18 ! [X2: option_trm,P: option_trm > option_fml > $o,Y2: option_fml] :
% 4.36/2.18 ( ( ( X2 = none_trm )
% 4.36/2.18 => ( P @ X2 @ Y2 ) )
% 4.36/2.18 => ( ( ( Y2 = none_fml )
% 4.36/2.18 => ( P @ X2 @ Y2 ) )
% 4.36/2.18 => ( ! [A5: trm,B5: fml] :
% 4.36/2.18 ( ( X2
% 4.36/2.18 = ( some_trm @ A5 ) )
% 4.36/2.18 => ( ( Y2
% 4.36/2.18 = ( some_fml @ B5 ) )
% 4.36/2.18 => ( P @ X2 @ Y2 ) ) )
% 4.36/2.18 => ( P @ X2 @ Y2 ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_111_combine__options__cases,axiom,
% 4.36/2.18 ! [X2: option_trm,P: option_trm > option_game > $o,Y2: option_game] :
% 4.36/2.18 ( ( ( X2 = none_trm )
% 4.36/2.18 => ( P @ X2 @ Y2 ) )
% 4.36/2.18 => ( ( ( Y2 = none_game )
% 4.36/2.18 => ( P @ X2 @ Y2 ) )
% 4.36/2.18 => ( ! [A5: trm,B5: game] :
% 4.36/2.18 ( ( X2
% 4.36/2.18 = ( some_trm @ A5 ) )
% 4.36/2.18 => ( ( Y2
% 4.36/2.18 = ( some_game @ B5 ) )
% 4.36/2.18 => ( P @ X2 @ Y2 ) ) )
% 4.36/2.18 => ( P @ X2 @ Y2 ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_112_combine__options__cases,axiom,
% 4.36/2.18 ! [X2: option_fml,P: option_fml > option_trm > $o,Y2: option_trm] :
% 4.36/2.18 ( ( ( X2 = none_fml )
% 4.36/2.18 => ( P @ X2 @ Y2 ) )
% 4.36/2.18 => ( ( ( Y2 = none_trm )
% 4.36/2.18 => ( P @ X2 @ Y2 ) )
% 4.36/2.18 => ( ! [A5: fml,B5: trm] :
% 4.36/2.18 ( ( X2
% 4.36/2.18 = ( some_fml @ A5 ) )
% 4.36/2.18 => ( ( Y2
% 4.36/2.18 = ( some_trm @ B5 ) )
% 4.36/2.18 => ( P @ X2 @ Y2 ) ) )
% 4.36/2.18 => ( P @ X2 @ Y2 ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_113_combine__options__cases,axiom,
% 4.36/2.18 ! [X2: option_fml,P: option_fml > option_fml > $o,Y2: option_fml] :
% 4.36/2.18 ( ( ( X2 = none_fml )
% 4.36/2.18 => ( P @ X2 @ Y2 ) )
% 4.36/2.18 => ( ( ( Y2 = none_fml )
% 4.36/2.18 => ( P @ X2 @ Y2 ) )
% 4.36/2.18 => ( ! [A5: fml,B5: fml] :
% 4.36/2.18 ( ( X2
% 4.36/2.18 = ( some_fml @ A5 ) )
% 4.36/2.18 => ( ( Y2
% 4.36/2.18 = ( some_fml @ B5 ) )
% 4.36/2.18 => ( P @ X2 @ Y2 ) ) )
% 4.36/2.18 => ( P @ X2 @ Y2 ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_114_combine__options__cases,axiom,
% 4.36/2.18 ! [X2: option_fml,P: option_fml > option_game > $o,Y2: option_game] :
% 4.36/2.18 ( ( ( X2 = none_fml )
% 4.36/2.18 => ( P @ X2 @ Y2 ) )
% 4.36/2.18 => ( ( ( Y2 = none_game )
% 4.36/2.18 => ( P @ X2 @ Y2 ) )
% 4.36/2.18 => ( ! [A5: fml,B5: game] :
% 4.36/2.18 ( ( X2
% 4.36/2.18 = ( some_fml @ A5 ) )
% 4.36/2.18 => ( ( Y2
% 4.36/2.18 = ( some_game @ B5 ) )
% 4.36/2.18 => ( P @ X2 @ Y2 ) ) )
% 4.36/2.18 => ( P @ X2 @ Y2 ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_115_combine__options__cases,axiom,
% 4.36/2.18 ! [X2: option_game,P: option_game > option_trm > $o,Y2: option_trm] :
% 4.36/2.18 ( ( ( X2 = none_game )
% 4.36/2.18 => ( P @ X2 @ Y2 ) )
% 4.36/2.18 => ( ( ( Y2 = none_trm )
% 4.36/2.18 => ( P @ X2 @ Y2 ) )
% 4.36/2.18 => ( ! [A5: game,B5: trm] :
% 4.36/2.18 ( ( X2
% 4.36/2.18 = ( some_game @ A5 ) )
% 4.36/2.18 => ( ( Y2
% 4.36/2.18 = ( some_trm @ B5 ) )
% 4.36/2.18 => ( P @ X2 @ Y2 ) ) )
% 4.36/2.18 => ( P @ X2 @ Y2 ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_116_combine__options__cases,axiom,
% 4.36/2.18 ! [X2: option_game,P: option_game > option_fml > $o,Y2: option_fml] :
% 4.36/2.18 ( ( ( X2 = none_game )
% 4.36/2.18 => ( P @ X2 @ Y2 ) )
% 4.36/2.18 => ( ( ( Y2 = none_fml )
% 4.36/2.18 => ( P @ X2 @ Y2 ) )
% 4.36/2.18 => ( ! [A5: game,B5: fml] :
% 4.36/2.18 ( ( X2
% 4.36/2.18 = ( some_game @ A5 ) )
% 4.36/2.18 => ( ( Y2
% 4.36/2.18 = ( some_fml @ B5 ) )
% 4.36/2.18 => ( P @ X2 @ Y2 ) ) )
% 4.36/2.18 => ( P @ X2 @ Y2 ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_117_combine__options__cases,axiom,
% 4.36/2.18 ! [X2: option_game,P: option_game > option_game > $o,Y2: option_game] :
% 4.36/2.18 ( ( ( X2 = none_game )
% 4.36/2.18 => ( P @ X2 @ Y2 ) )
% 4.36/2.18 => ( ( ( Y2 = none_game )
% 4.36/2.18 => ( P @ X2 @ Y2 ) )
% 4.36/2.18 => ( ! [A5: game,B5: game] :
% 4.36/2.18 ( ( X2
% 4.36/2.18 = ( some_game @ A5 ) )
% 4.36/2.18 => ( ( Y2
% 4.36/2.18 = ( some_game @ B5 ) )
% 4.36/2.18 => ( P @ X2 @ Y2 ) ) )
% 4.36/2.18 => ( P @ X2 @ Y2 ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_118_split__option__all,axiom,
% 4.36/2.18 ( ( ^ [P2: option_trm > $o] :
% 4.36/2.18 ! [X5: option_trm] : ( P2 @ X5 ) )
% 4.36/2.18 = ( ^ [P3: option_trm > $o] :
% 4.36/2.18 ( ( P3 @ none_trm )
% 4.36/2.18 & ! [X3: trm] : ( P3 @ ( some_trm @ X3 ) ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_119_split__option__all,axiom,
% 4.36/2.18 ( ( ^ [P2: option_fml > $o] :
% 4.36/2.18 ! [X5: option_fml] : ( P2 @ X5 ) )
% 4.36/2.18 = ( ^ [P3: option_fml > $o] :
% 4.36/2.18 ( ( P3 @ none_fml )
% 4.36/2.18 & ! [X3: fml] : ( P3 @ ( some_fml @ X3 ) ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_120_split__option__all,axiom,
% 4.36/2.18 ( ( ^ [P2: option_game > $o] :
% 4.36/2.18 ! [X5: option_game] : ( P2 @ X5 ) )
% 4.36/2.18 = ( ^ [P3: option_game > $o] :
% 4.36/2.18 ( ( P3 @ none_game )
% 4.36/2.18 & ! [X3: game] : ( P3 @ ( some_game @ X3 ) ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_121_split__option__ex,axiom,
% 4.36/2.18 ( ( ^ [P2: option_trm > $o] :
% 4.36/2.18 ? [X5: option_trm] : ( P2 @ X5 ) )
% 4.36/2.18 = ( ^ [P3: option_trm > $o] :
% 4.36/2.18 ( ( P3 @ none_trm )
% 4.36/2.18 | ? [X3: trm] : ( P3 @ ( some_trm @ X3 ) ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_122_split__option__ex,axiom,
% 4.36/2.18 ( ( ^ [P2: option_fml > $o] :
% 4.36/2.18 ? [X5: option_fml] : ( P2 @ X5 ) )
% 4.36/2.18 = ( ^ [P3: option_fml > $o] :
% 4.36/2.18 ( ( P3 @ none_fml )
% 4.36/2.18 | ? [X3: fml] : ( P3 @ ( some_fml @ X3 ) ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_123_split__option__ex,axiom,
% 4.36/2.18 ( ( ^ [P2: option_game > $o] :
% 4.36/2.18 ? [X5: option_game] : ( P2 @ X5 ) )
% 4.36/2.18 = ( ^ [P3: option_game > $o] :
% 4.36/2.18 ( ( P3 @ none_game )
% 4.36/2.18 | ? [X3: game] : ( P3 @ ( some_game @ X3 ) ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_124_option_Oinducts,axiom,
% 4.36/2.18 ! [P: option_trm > $o,Option: option_trm] :
% 4.36/2.18 ( ( P @ none_trm )
% 4.36/2.18 => ( ! [X: trm] : ( P @ ( some_trm @ X ) )
% 4.36/2.18 => ( P @ Option ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_125_option_Oinducts,axiom,
% 4.36/2.18 ! [P: option_fml > $o,Option: option_fml] :
% 4.36/2.18 ( ( P @ none_fml )
% 4.36/2.18 => ( ! [X: fml] : ( P @ ( some_fml @ X ) )
% 4.36/2.18 => ( P @ Option ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_126_option_Oinducts,axiom,
% 4.36/2.18 ! [P: option_game > $o,Option: option_game] :
% 4.36/2.18 ( ( P @ none_game )
% 4.36/2.18 => ( ! [X: game] : ( P @ ( some_game @ X ) )
% 4.36/2.18 => ( P @ Option ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_127_option_Oexhaust,axiom,
% 4.36/2.18 ! [Y2: option_trm] :
% 4.36/2.18 ( ( Y2 != none_trm )
% 4.36/2.18 => ~ ! [X24: trm] :
% 4.36/2.18 ( Y2
% 4.36/2.18 != ( some_trm @ X24 ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_128_option_Oexhaust,axiom,
% 4.36/2.18 ! [Y2: option_fml] :
% 4.36/2.18 ( ( Y2 != none_fml )
% 4.36/2.18 => ~ ! [X24: fml] :
% 4.36/2.18 ( Y2
% 4.36/2.18 != ( some_fml @ X24 ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_129_option_Oexhaust,axiom,
% 4.36/2.18 ! [Y2: option_game] :
% 4.36/2.18 ( ( Y2 != none_game )
% 4.36/2.18 => ~ ! [X24: game] :
% 4.36/2.18 ( Y2
% 4.36/2.18 != ( some_game @ X24 ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_130_option_OdiscI,axiom,
% 4.36/2.18 ! [Option: option_trm,X23: trm] :
% 4.36/2.18 ( ( Option
% 4.36/2.18 = ( some_trm @ X23 ) )
% 4.36/2.18 => ( Option != none_trm ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_131_option_OdiscI,axiom,
% 4.36/2.18 ! [Option: option_fml,X23: fml] :
% 4.36/2.18 ( ( Option
% 4.36/2.18 = ( some_fml @ X23 ) )
% 4.36/2.18 => ( Option != none_fml ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_132_option_OdiscI,axiom,
% 4.36/2.18 ! [Option: option_game,X23: game] :
% 4.36/2.18 ( ( Option
% 4.36/2.18 = ( some_game @ X23 ) )
% 4.36/2.18 => ( Option != none_game ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_133_option_Odistinct_I1_J,axiom,
% 4.36/2.18 ! [X23: trm] :
% 4.36/2.18 ( none_trm
% 4.36/2.18 != ( some_trm @ X23 ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_134_option_Odistinct_I1_J,axiom,
% 4.36/2.18 ! [X23: fml] :
% 4.36/2.18 ( none_fml
% 4.36/2.18 != ( some_fml @ X23 ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_135_option_Odistinct_I1_J,axiom,
% 4.36/2.18 ! [X23: game] :
% 4.36/2.18 ( none_game
% 4.36/2.18 != ( some_game @ X23 ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_136_Differentialo_Oinduct,axiom,
% 4.36/2.18 ! [P: option_trm > $o,A0: option_trm] :
% 4.36/2.18 ( ! [Theta2: trm] : ( P @ ( some_trm @ Theta2 ) )
% 4.36/2.18 => ( ( P @ none_trm )
% 4.36/2.18 => ( P @ A0 ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_137_Differentialo_Ocases,axiom,
% 4.36/2.18 ! [X2: option_trm] :
% 4.36/2.18 ( ! [Theta2: trm] :
% 4.36/2.18 ( X2
% 4.36/2.18 != ( some_trm @ Theta2 ) )
% 4.36/2.18 => ( X2 = none_trm ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_138_Assigno_Oinduct,axiom,
% 4.36/2.18 ! [P: variable > option_trm > $o,A0: variable,A1: option_trm] :
% 4.36/2.18 ( ! [X: variable,Theta2: trm] : ( P @ X @ ( some_trm @ Theta2 ) )
% 4.36/2.18 => ( ! [X: variable] : ( P @ X @ none_trm )
% 4.36/2.18 => ( P @ A0 @ A1 ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_139_Timeso_Oinduct,axiom,
% 4.36/2.18 ! [P: option_trm > option_trm > $o,A0: option_trm,A1: option_trm] :
% 4.36/2.18 ( ! [Theta2: trm,Eta2: trm] : ( P @ ( some_trm @ Theta2 ) @ ( some_trm @ Eta2 ) )
% 4.36/2.18 => ( ! [X_1: option_trm] : ( P @ none_trm @ X_1 )
% 4.36/2.18 => ( ! [V2: trm] : ( P @ ( some_trm @ V2 ) @ none_trm )
% 4.36/2.18 => ( P @ A0 @ A1 ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_140_undeft__equiv,axiom,
% 4.36/2.18 ! [Theta: option_trm] :
% 4.36/2.18 ( ( Theta != none_trm )
% 4.36/2.18 = ( ? [T: trm] :
% 4.36/2.18 ( Theta
% 4.36/2.18 = ( some_trm @ T ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_141_ODEo_Oinduct,axiom,
% 4.36/2.18 ! [P: char > option_trm > $o,A0: char,A1: option_trm] :
% 4.36/2.18 ( ! [X: char,Theta2: trm] : ( P @ X @ ( some_trm @ Theta2 ) )
% 4.36/2.18 => ( ! [X: char] : ( P @ X @ none_trm )
% 4.36/2.18 => ( P @ A0 @ A1 ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_142_Differentialo_Oelims,axiom,
% 4.36/2.18 ! [X2: option_trm,Y2: option_trm] :
% 4.36/2.18 ( ( ( uSubst716837505ntialo @ X2 )
% 4.36/2.18 = Y2 )
% 4.36/2.18 => ( ! [Theta2: trm] :
% 4.36/2.18 ( ( X2
% 4.36/2.18 = ( some_trm @ Theta2 ) )
% 4.36/2.18 => ( Y2
% 4.36/2.18 != ( some_trm @ ( differential @ Theta2 ) ) ) )
% 4.36/2.18 => ~ ( ( X2 = none_trm )
% 4.36/2.18 => ( Y2 != none_trm ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_143_trm_Odistinct_I41_J,axiom,
% 4.36/2.18 ! [X61: trm,X62: trm,X7: trm] :
% 4.36/2.18 ( ( times @ X61 @ X62 )
% 4.36/2.18 != ( differential @ X7 ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_144_trm_Odistinct_I39_J,axiom,
% 4.36/2.18 ! [X51: trm,X52: trm,X7: trm] :
% 4.36/2.18 ( ( plus @ X51 @ X52 )
% 4.36/2.18 != ( differential @ X7 ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_145_Timeso_Osimps_I3_J,axiom,
% 4.36/2.18 ! [V3: trm] :
% 4.36/2.18 ( ( uSubst918876924Timeso @ ( some_trm @ V3 ) @ none_trm )
% 4.36/2.18 = none_trm ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_146_Pluso_Osimps_I3_J,axiom,
% 4.36/2.18 ! [V3: trm] :
% 4.36/2.18 ( ( uSubst141955042_Pluso @ ( some_trm @ V3 ) @ none_trm )
% 4.36/2.18 = none_trm ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_147_Pluso_Osimps_I1_J,axiom,
% 4.36/2.18 ! [Theta: trm,Eta: trm] :
% 4.36/2.18 ( ( uSubst141955042_Pluso @ ( some_trm @ Theta ) @ ( some_trm @ Eta ) )
% 4.36/2.18 = ( some_trm @ ( plus @ Theta @ Eta ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_148_Timeso_Osimps_I1_J,axiom,
% 4.36/2.18 ! [Theta: trm,Eta: trm] :
% 4.36/2.18 ( ( uSubst918876924Timeso @ ( some_trm @ Theta ) @ ( some_trm @ Eta ) )
% 4.36/2.18 = ( some_trm @ ( times @ Theta @ Eta ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_149_usubstappt__differential__conv,axiom,
% 4.36/2.18 ! [Sigma: produc1418842292n_game,U: set_variable,Theta: trm] :
% 4.36/2.18 ( ( ( uSubst516392818stappt @ Sigma @ U @ ( differential @ Theta ) )
% 4.36/2.18 != none_trm )
% 4.36/2.18 => ( ( uSubst516392818stappt @ Sigma
% 4.36/2.18 @ ( collect_variable
% 4.36/2.18 @ ^ [X3: variable] : $true )
% 4.36/2.18 @ Theta )
% 4.36/2.18 != none_trm ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_150_Geqo_Osimps_I3_J,axiom,
% 4.36/2.18 ! [V3: trm] :
% 4.36/2.18 ( ( uSubst152838031e_Geqo @ ( some_trm @ V3 ) @ none_trm )
% 4.36/2.18 = none_fml ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_151_Geqo_Oelims,axiom,
% 4.36/2.18 ! [X2: option_trm,Xa: option_trm,Y2: option_fml] :
% 4.36/2.18 ( ( ( uSubst152838031e_Geqo @ X2 @ Xa )
% 4.36/2.18 = Y2 )
% 4.36/2.18 => ( ! [Theta2: trm] :
% 4.36/2.18 ( ( X2
% 4.36/2.18 = ( some_trm @ Theta2 ) )
% 4.36/2.18 => ! [Eta2: trm] :
% 4.36/2.18 ( ( Xa
% 4.36/2.18 = ( some_trm @ Eta2 ) )
% 4.36/2.18 => ( Y2
% 4.36/2.18 != ( some_fml @ ( geq @ Theta2 @ Eta2 ) ) ) ) )
% 4.36/2.18 => ( ( ( X2 = none_trm )
% 4.36/2.18 => ( Y2 != none_fml ) )
% 4.36/2.18 => ~ ( ? [V2: trm] :
% 4.36/2.18 ( X2
% 4.36/2.18 = ( some_trm @ V2 ) )
% 4.36/2.18 => ( ( Xa = none_trm )
% 4.36/2.18 => ( Y2 != none_fml ) ) ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_152_Differentialo_Opelims,axiom,
% 4.36/2.18 ! [X2: option_trm,Y2: option_trm] :
% 4.36/2.18 ( ( ( uSubst716837505ntialo @ X2 )
% 4.36/2.18 = Y2 )
% 4.36/2.18 => ( ( accp_option_trm @ uSubst2051024824lo_rel @ X2 )
% 4.36/2.18 => ( ! [Theta2: trm] :
% 4.36/2.18 ( ( X2
% 4.36/2.18 = ( some_trm @ Theta2 ) )
% 4.36/2.18 => ( ( Y2
% 4.36/2.18 = ( some_trm @ ( differential @ Theta2 ) ) )
% 4.36/2.18 => ~ ( accp_option_trm @ uSubst2051024824lo_rel @ ( some_trm @ Theta2 ) ) ) )
% 4.36/2.18 => ~ ( ( X2 = none_trm )
% 4.36/2.18 => ( ( Y2 = none_trm )
% 4.36/2.18 => ~ ( accp_option_trm @ uSubst2051024824lo_rel @ none_trm ) ) ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_153_Geqo_Osimps_I1_J,axiom,
% 4.36/2.18 ! [Theta: trm,Eta: trm] :
% 4.36/2.18 ( ( uSubst152838031e_Geqo @ ( some_trm @ Theta ) @ ( some_trm @ Eta ) )
% 4.36/2.18 = ( some_fml @ ( geq @ Theta @ Eta ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_154_GreatestI2__order,axiom,
% 4.36/2.18 ! [P: set_variable > $o,X2: set_variable,Q: set_variable > $o] :
% 4.36/2.18 ( ( P @ X2 )
% 4.36/2.18 => ( ! [Y4: set_variable] :
% 4.36/2.18 ( ( P @ Y4 )
% 4.36/2.18 => ( ord_le282106107riable @ Y4 @ X2 ) )
% 4.36/2.18 => ( ! [X: set_variable] :
% 4.36/2.18 ( ( P @ X )
% 4.36/2.18 => ( ! [Y5: set_variable] :
% 4.36/2.18 ( ( P @ Y5 )
% 4.36/2.18 => ( ord_le282106107riable @ Y5 @ X ) )
% 4.36/2.18 => ( Q @ X ) ) )
% 4.36/2.18 => ( Q @ ( order_272405634riable @ P ) ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_155_Greatest__equality,axiom,
% 4.36/2.18 ! [P: set_variable > $o,X2: set_variable] :
% 4.36/2.18 ( ( P @ X2 )
% 4.36/2.18 => ( ! [Y4: set_variable] :
% 4.36/2.18 ( ( P @ Y4 )
% 4.36/2.18 => ( ord_le282106107riable @ Y4 @ X2 ) )
% 4.36/2.18 => ( ( order_272405634riable @ P )
% 4.36/2.18 = X2 ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_156_Diamondo_Oinduct,axiom,
% 4.36/2.18 ! [P: option_game > option_fml > $o,A0: option_game,A1: option_fml] :
% 4.36/2.18 ( ! [Alpha: game,Phi2: fml] : ( P @ ( some_game @ Alpha ) @ ( some_fml @ Phi2 ) )
% 4.36/2.18 => ( ! [X_1: option_fml] : ( P @ none_game @ X_1 )
% 4.36/2.18 => ( ! [V2: game] : ( P @ ( some_game @ V2 ) @ none_fml )
% 4.36/2.18 => ( P @ A0 @ A1 ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_157_Existso_Oinduct,axiom,
% 4.36/2.18 ! [P: variable > option_fml > $o,A0: variable,A1: option_fml] :
% 4.36/2.18 ( ! [X: variable,Phi2: fml] : ( P @ X @ ( some_fml @ Phi2 ) )
% 4.36/2.18 => ( ! [X: variable] : ( P @ X @ none_fml )
% 4.36/2.18 => ( P @ A0 @ A1 ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_158_undeff__equiv,axiom,
% 4.36/2.18 ! [Phi: option_fml] :
% 4.36/2.18 ( ( Phi != none_fml )
% 4.36/2.18 = ( ? [F2: fml] :
% 4.36/2.18 ( Phi
% 4.36/2.18 = ( some_fml @ F2 ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_159_Testo_Oinduct,axiom,
% 4.36/2.18 ! [P: option_fml > $o,A0: option_fml] :
% 4.36/2.18 ( ! [Phi2: fml] : ( P @ ( some_fml @ Phi2 ) )
% 4.36/2.18 => ( ( P @ none_fml )
% 4.36/2.18 => ( P @ A0 ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_160_Testo_Ocases,axiom,
% 4.36/2.18 ! [X2: option_fml] :
% 4.36/2.18 ( ! [Phi2: fml] :
% 4.36/2.18 ( X2
% 4.36/2.18 != ( some_fml @ Phi2 ) )
% 4.36/2.18 => ( X2 = none_fml ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_161_Ando_Oinduct,axiom,
% 4.36/2.18 ! [P: option_fml > option_fml > $o,A0: option_fml,A1: option_fml] :
% 4.36/2.18 ( ! [Phi2: fml,Psi: fml] : ( P @ ( some_fml @ Phi2 ) @ ( some_fml @ Psi ) )
% 4.36/2.18 => ( ! [X_1: option_fml] : ( P @ none_fml @ X_1 )
% 4.36/2.18 => ( ! [V2: fml] : ( P @ ( some_fml @ V2 ) @ none_fml )
% 4.36/2.18 => ( P @ A0 @ A1 ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_162_accp__subset,axiom,
% 4.36/2.18 ! [R1: produc1024976764on_trm > produc1024976764on_trm > $o,R2: produc1024976764on_trm > produc1024976764on_trm > $o] :
% 4.36/2.18 ( ( ord_le370603054_trm_o @ R1 @ R2 )
% 4.36/2.18 => ( ord_le373274227_trm_o @ ( accp_P394694195on_trm @ R2 ) @ ( accp_P394694195on_trm @ R1 ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_163_accp__subset,axiom,
% 4.36/2.18 ! [R1: produc1072747943on_trm > produc1072747943on_trm > $o,R2: produc1072747943on_trm > produc1072747943on_trm > $o] :
% 4.36/2.18 ( ( ord_le90123726_trm_o @ R1 @ R2 )
% 4.36/2.18 => ( ord_le1721128566_trm_o @ ( accp_P758790320on_trm @ R2 ) @ ( accp_P758790320on_trm @ R1 ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_164_accp__subset,axiom,
% 4.36/2.18 ! [R1: produc464795408on_trm > produc464795408on_trm > $o,R2: produc464795408on_trm > produc464795408on_trm > $o] :
% 4.36/2.18 ( ( ord_le157637894_trm_o @ R1 @ R2 )
% 4.36/2.18 => ( ord_le1222882015_trm_o @ ( accp_P419951815on_trm @ R2 ) @ ( accp_P419951815on_trm @ R1 ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_165_accp__subset,axiom,
% 4.36/2.18 ! [R1: option_trm > option_trm > $o,R2: option_trm > option_trm > $o] :
% 4.36/2.18 ( ( ord_le847028878_trm_o @ R1 @ R2 )
% 4.36/2.18 => ( ord_le1957133745_trm_o @ ( accp_option_trm @ R2 ) @ ( accp_option_trm @ R1 ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_166_accp__subset,axiom,
% 4.36/2.18 ! [R1: option_fml > option_fml > $o,R2: option_fml > option_fml > $o] :
% 4.36/2.18 ( ( ord_le802833166_fml_o @ R1 @ R2 )
% 4.36/2.18 => ( ord_le181580155_fml_o @ ( accp_option_fml @ R2 ) @ ( accp_option_fml @ R1 ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_167_accp__subset__induct,axiom,
% 4.36/2.18 ! [D: produc1024976764on_trm > $o,R: produc1024976764on_trm > produc1024976764on_trm > $o,X2: produc1024976764on_trm,P: produc1024976764on_trm > $o] :
% 4.36/2.18 ( ( ord_le373274227_trm_o @ D @ ( accp_P394694195on_trm @ R ) )
% 4.36/2.18 => ( ! [X: produc1024976764on_trm,Z4: produc1024976764on_trm] :
% 4.36/2.18 ( ( D @ X )
% 4.36/2.18 => ( ( R @ Z4 @ X )
% 4.36/2.18 => ( D @ Z4 ) ) )
% 4.36/2.18 => ( ( D @ X2 )
% 4.36/2.18 => ( ! [X: produc1024976764on_trm] :
% 4.36/2.18 ( ( D @ X )
% 4.36/2.18 => ( ! [Z5: produc1024976764on_trm] :
% 4.36/2.18 ( ( R @ Z5 @ X )
% 4.36/2.18 => ( P @ Z5 ) )
% 4.36/2.18 => ( P @ X ) ) )
% 4.36/2.18 => ( P @ X2 ) ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_168_accp__subset__induct,axiom,
% 4.36/2.18 ! [D: produc1072747943on_trm > $o,R: produc1072747943on_trm > produc1072747943on_trm > $o,X2: produc1072747943on_trm,P: produc1072747943on_trm > $o] :
% 4.36/2.18 ( ( ord_le1721128566_trm_o @ D @ ( accp_P758790320on_trm @ R ) )
% 4.36/2.18 => ( ! [X: produc1072747943on_trm,Z4: produc1072747943on_trm] :
% 4.36/2.18 ( ( D @ X )
% 4.36/2.18 => ( ( R @ Z4 @ X )
% 4.36/2.18 => ( D @ Z4 ) ) )
% 4.36/2.18 => ( ( D @ X2 )
% 4.36/2.18 => ( ! [X: produc1072747943on_trm] :
% 4.36/2.18 ( ( D @ X )
% 4.36/2.18 => ( ! [Z5: produc1072747943on_trm] :
% 4.36/2.18 ( ( R @ Z5 @ X )
% 4.36/2.18 => ( P @ Z5 ) )
% 4.36/2.18 => ( P @ X ) ) )
% 4.36/2.18 => ( P @ X2 ) ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_169_accp__subset__induct,axiom,
% 4.36/2.18 ! [D: produc464795408on_trm > $o,R: produc464795408on_trm > produc464795408on_trm > $o,X2: produc464795408on_trm,P: produc464795408on_trm > $o] :
% 4.36/2.18 ( ( ord_le1222882015_trm_o @ D @ ( accp_P419951815on_trm @ R ) )
% 4.36/2.18 => ( ! [X: produc464795408on_trm,Z4: produc464795408on_trm] :
% 4.36/2.18 ( ( D @ X )
% 4.36/2.18 => ( ( R @ Z4 @ X )
% 4.36/2.18 => ( D @ Z4 ) ) )
% 4.36/2.18 => ( ( D @ X2 )
% 4.36/2.18 => ( ! [X: produc464795408on_trm] :
% 4.36/2.18 ( ( D @ X )
% 4.36/2.18 => ( ! [Z5: produc464795408on_trm] :
% 4.36/2.18 ( ( R @ Z5 @ X )
% 4.36/2.18 => ( P @ Z5 ) )
% 4.36/2.18 => ( P @ X ) ) )
% 4.36/2.18 => ( P @ X2 ) ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_170_accp__subset__induct,axiom,
% 4.36/2.18 ! [D: option_trm > $o,R: option_trm > option_trm > $o,X2: option_trm,P: option_trm > $o] :
% 4.36/2.18 ( ( ord_le1957133745_trm_o @ D @ ( accp_option_trm @ R ) )
% 4.36/2.18 => ( ! [X: option_trm,Z4: option_trm] :
% 4.36/2.18 ( ( D @ X )
% 4.36/2.18 => ( ( R @ Z4 @ X )
% 4.36/2.18 => ( D @ Z4 ) ) )
% 4.36/2.18 => ( ( D @ X2 )
% 4.36/2.18 => ( ! [X: option_trm] :
% 4.36/2.18 ( ( D @ X )
% 4.36/2.18 => ( ! [Z5: option_trm] :
% 4.36/2.18 ( ( R @ Z5 @ X )
% 4.36/2.18 => ( P @ Z5 ) )
% 4.36/2.18 => ( P @ X ) ) )
% 4.36/2.18 => ( P @ X2 ) ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_171_accp__subset__induct,axiom,
% 4.36/2.18 ! [D: option_fml > $o,R: option_fml > option_fml > $o,X2: option_fml,P: option_fml > $o] :
% 4.36/2.18 ( ( ord_le181580155_fml_o @ D @ ( accp_option_fml @ R ) )
% 4.36/2.18 => ( ! [X: option_fml,Z4: option_fml] :
% 4.36/2.18 ( ( D @ X )
% 4.36/2.18 => ( ( R @ Z4 @ X )
% 4.36/2.18 => ( D @ Z4 ) ) )
% 4.36/2.18 => ( ( D @ X2 )
% 4.36/2.18 => ( ! [X: option_fml] :
% 4.36/2.18 ( ( D @ X )
% 4.36/2.18 => ( ! [Z5: option_fml] :
% 4.36/2.18 ( ( R @ Z5 @ X )
% 4.36/2.18 => ( P @ Z5 ) )
% 4.36/2.18 => ( P @ X ) ) )
% 4.36/2.18 => ( P @ X2 ) ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_172_usubstappf__geqr,axiom,
% 4.36/2.18 ! [Sigma: produc1418842292n_game,U: set_variable,Theta: trm,Eta: trm] :
% 4.36/2.18 ( ( ( uSubst516392804stappf @ Sigma @ U @ ( geq @ Theta @ Eta ) )
% 4.36/2.18 != none_fml )
% 4.36/2.18 => ( ( uSubst516392804stappf @ Sigma @ U @ ( geq @ Theta @ Eta ) )
% 4.36/2.18 = ( some_fml @ ( geq @ ( the_trm @ ( uSubst516392818stappt @ Sigma @ U @ Theta ) ) @ ( the_trm @ ( uSubst516392818stappt @ Sigma @ U @ Eta ) ) ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_173_usubstappf__geq,axiom,
% 4.36/2.18 ! [Sigma: produc1418842292n_game,U: set_variable,Theta: trm,Eta: trm] :
% 4.36/2.18 ( ( ( uSubst516392818stappt @ Sigma @ U @ Theta )
% 4.36/2.18 != none_trm )
% 4.36/2.18 => ( ( ( uSubst516392818stappt @ Sigma @ U @ Eta )
% 4.36/2.18 != none_trm )
% 4.36/2.18 => ( ( uSubst516392804stappf @ Sigma @ U @ ( geq @ Theta @ Eta ) )
% 4.36/2.18 = ( some_fml @ ( geq @ ( the_trm @ ( uSubst516392818stappt @ Sigma @ U @ Theta ) ) @ ( the_trm @ ( uSubst516392818stappt @ Sigma @ U @ Eta ) ) ) ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_174_option_Ocollapse,axiom,
% 4.36/2.18 ! [Option: option_trm] :
% 4.36/2.18 ( ( Option != none_trm )
% 4.36/2.18 => ( ( some_trm @ ( the_trm @ Option ) )
% 4.36/2.18 = Option ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_175_option_Ocollapse,axiom,
% 4.36/2.18 ! [Option: option_fml] :
% 4.36/2.18 ( ( Option != none_fml )
% 4.36/2.18 => ( ( some_fml @ ( the_fml @ Option ) )
% 4.36/2.18 = Option ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_176_option_Ocollapse,axiom,
% 4.36/2.18 ! [Option: option_game] :
% 4.36/2.18 ( ( Option != none_game )
% 4.36/2.18 => ( ( some_game @ ( the_game @ Option ) )
% 4.36/2.18 = Option ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_177_Composeo_Oinduct,axiom,
% 4.36/2.18 ! [P: option_game > option_game > $o,A0: option_game,A1: option_game] :
% 4.36/2.18 ( ! [Alpha: game,Beta: game] : ( P @ ( some_game @ Alpha ) @ ( some_game @ Beta ) )
% 4.36/2.18 => ( ! [Alpha: option_game] : ( P @ Alpha @ none_game )
% 4.36/2.18 => ( ! [V2: game] : ( P @ none_game @ ( some_game @ V2 ) )
% 4.36/2.18 => ( P @ A0 @ A1 ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_178_undefg__equiv,axiom,
% 4.36/2.18 ! [Alpha2: option_game] :
% 4.36/2.18 ( ( Alpha2 != none_game )
% 4.36/2.18 = ( ? [G: game] :
% 4.36/2.18 ( Alpha2
% 4.36/2.18 = ( some_game @ G ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_179_Loopo_Oinduct,axiom,
% 4.36/2.18 ! [P: option_game > $o,A0: option_game] :
% 4.36/2.18 ( ! [Alpha: game] : ( P @ ( some_game @ Alpha ) )
% 4.36/2.18 => ( ( P @ none_game )
% 4.36/2.18 => ( P @ A0 ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_180_Loopo_Ocases,axiom,
% 4.36/2.18 ! [X2: option_game] :
% 4.36/2.18 ( ! [Alpha: game] :
% 4.36/2.18 ( X2
% 4.36/2.18 != ( some_game @ Alpha ) )
% 4.36/2.18 => ( X2 = none_game ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_181_option_Oexpand,axiom,
% 4.36/2.18 ! [Option: option_trm,Option2: option_trm] :
% 4.36/2.18 ( ( ( Option = none_trm )
% 4.36/2.18 = ( Option2 = none_trm ) )
% 4.36/2.18 => ( ( ( Option != none_trm )
% 4.36/2.18 => ( ( Option2 != none_trm )
% 4.36/2.18 => ( ( the_trm @ Option )
% 4.36/2.18 = ( the_trm @ Option2 ) ) ) )
% 4.36/2.18 => ( Option = Option2 ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_182_option_Oexpand,axiom,
% 4.36/2.18 ! [Option: option_fml,Option2: option_fml] :
% 4.36/2.18 ( ( ( Option = none_fml )
% 4.36/2.18 = ( Option2 = none_fml ) )
% 4.36/2.18 => ( ( ( Option != none_fml )
% 4.36/2.18 => ( ( Option2 != none_fml )
% 4.36/2.18 => ( ( the_fml @ Option )
% 4.36/2.18 = ( the_fml @ Option2 ) ) ) )
% 4.36/2.18 => ( Option = Option2 ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_183_option_Oexpand,axiom,
% 4.36/2.18 ! [Option: option_game,Option2: option_game] :
% 4.36/2.18 ( ( ( Option = none_game )
% 4.36/2.18 = ( Option2 = none_game ) )
% 4.36/2.18 => ( ( ( Option != none_game )
% 4.36/2.18 => ( ( Option2 != none_game )
% 4.36/2.18 => ( ( the_game @ Option )
% 4.36/2.18 = ( the_game @ Option2 ) ) ) )
% 4.36/2.18 => ( Option = Option2 ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_184_option_Osel,axiom,
% 4.36/2.18 ! [X23: trm] :
% 4.36/2.18 ( ( the_trm @ ( some_trm @ X23 ) )
% 4.36/2.18 = X23 ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_185_option_Osel,axiom,
% 4.36/2.18 ! [X23: fml] :
% 4.36/2.18 ( ( the_fml @ ( some_fml @ X23 ) )
% 4.36/2.18 = X23 ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_186_option_Osel,axiom,
% 4.36/2.18 ! [X23: game] :
% 4.36/2.18 ( ( the_game @ ( some_game @ X23 ) )
% 4.36/2.18 = X23 ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_187_option_Oexhaust__sel,axiom,
% 4.36/2.18 ! [Option: option_trm] :
% 4.36/2.18 ( ( Option != none_trm )
% 4.36/2.18 => ( Option
% 4.36/2.18 = ( some_trm @ ( the_trm @ Option ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_188_option_Oexhaust__sel,axiom,
% 4.36/2.18 ! [Option: option_fml] :
% 4.36/2.18 ( ( Option != none_fml )
% 4.36/2.18 => ( Option
% 4.36/2.18 = ( some_fml @ ( the_fml @ Option ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_189_option_Oexhaust__sel,axiom,
% 4.36/2.18 ! [Option: option_game] :
% 4.36/2.18 ( ( Option != none_game )
% 4.36/2.18 => ( Option
% 4.36/2.18 = ( some_game @ ( the_game @ Option ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_190_accp_Ocases,axiom,
% 4.36/2.18 ! [R3: produc1024976764on_trm > produc1024976764on_trm > $o,A3: produc1024976764on_trm] :
% 4.36/2.18 ( ( accp_P394694195on_trm @ R3 @ A3 )
% 4.36/2.18 => ! [Y5: produc1024976764on_trm] :
% 4.36/2.18 ( ( R3 @ Y5 @ A3 )
% 4.36/2.18 => ( accp_P394694195on_trm @ R3 @ Y5 ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_191_accp_Ocases,axiom,
% 4.36/2.18 ! [R3: produc1072747943on_trm > produc1072747943on_trm > $o,A3: produc1072747943on_trm] :
% 4.36/2.18 ( ( accp_P758790320on_trm @ R3 @ A3 )
% 4.36/2.18 => ! [Y5: produc1072747943on_trm] :
% 4.36/2.18 ( ( R3 @ Y5 @ A3 )
% 4.36/2.18 => ( accp_P758790320on_trm @ R3 @ Y5 ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_192_accp_Ocases,axiom,
% 4.36/2.18 ! [R3: produc464795408on_trm > produc464795408on_trm > $o,A3: produc464795408on_trm] :
% 4.36/2.18 ( ( accp_P419951815on_trm @ R3 @ A3 )
% 4.36/2.18 => ! [Y5: produc464795408on_trm] :
% 4.36/2.18 ( ( R3 @ Y5 @ A3 )
% 4.36/2.18 => ( accp_P419951815on_trm @ R3 @ Y5 ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_193_accp_Ocases,axiom,
% 4.36/2.18 ! [R3: option_trm > option_trm > $o,A3: option_trm] :
% 4.36/2.18 ( ( accp_option_trm @ R3 @ A3 )
% 4.36/2.18 => ! [Y5: option_trm] :
% 4.36/2.18 ( ( R3 @ Y5 @ A3 )
% 4.36/2.18 => ( accp_option_trm @ R3 @ Y5 ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_194_accp_Ocases,axiom,
% 4.36/2.18 ! [R3: option_fml > option_fml > $o,A3: option_fml] :
% 4.36/2.18 ( ( accp_option_fml @ R3 @ A3 )
% 4.36/2.18 => ! [Y5: option_fml] :
% 4.36/2.18 ( ( R3 @ Y5 @ A3 )
% 4.36/2.18 => ( accp_option_fml @ R3 @ Y5 ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_195_accp_Osimps,axiom,
% 4.36/2.18 ( accp_P394694195on_trm
% 4.36/2.18 = ( ^ [R4: produc1024976764on_trm > produc1024976764on_trm > $o,A4: produc1024976764on_trm] :
% 4.36/2.18 ? [X3: produc1024976764on_trm] :
% 4.36/2.18 ( ( A4 = X3 )
% 4.36/2.18 & ! [Y3: produc1024976764on_trm] :
% 4.36/2.18 ( ( R4 @ Y3 @ X3 )
% 4.36/2.18 => ( accp_P394694195on_trm @ R4 @ Y3 ) ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_196_accp_Osimps,axiom,
% 4.36/2.18 ( accp_P758790320on_trm
% 4.36/2.18 = ( ^ [R4: produc1072747943on_trm > produc1072747943on_trm > $o,A4: produc1072747943on_trm] :
% 4.36/2.18 ? [X3: produc1072747943on_trm] :
% 4.36/2.18 ( ( A4 = X3 )
% 4.36/2.18 & ! [Y3: produc1072747943on_trm] :
% 4.36/2.18 ( ( R4 @ Y3 @ X3 )
% 4.36/2.18 => ( accp_P758790320on_trm @ R4 @ Y3 ) ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_197_accp_Osimps,axiom,
% 4.36/2.18 ( accp_P419951815on_trm
% 4.36/2.18 = ( ^ [R4: produc464795408on_trm > produc464795408on_trm > $o,A4: produc464795408on_trm] :
% 4.36/2.18 ? [X3: produc464795408on_trm] :
% 4.36/2.18 ( ( A4 = X3 )
% 4.36/2.18 & ! [Y3: produc464795408on_trm] :
% 4.36/2.18 ( ( R4 @ Y3 @ X3 )
% 4.36/2.18 => ( accp_P419951815on_trm @ R4 @ Y3 ) ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_198_accp_Osimps,axiom,
% 4.36/2.18 ( accp_option_trm
% 4.36/2.18 = ( ^ [R4: option_trm > option_trm > $o,A4: option_trm] :
% 4.36/2.18 ? [X3: option_trm] :
% 4.36/2.18 ( ( A4 = X3 )
% 4.36/2.18 & ! [Y3: option_trm] :
% 4.36/2.18 ( ( R4 @ Y3 @ X3 )
% 4.36/2.18 => ( accp_option_trm @ R4 @ Y3 ) ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_199_accp_Osimps,axiom,
% 4.36/2.18 ( accp_option_fml
% 4.36/2.18 = ( ^ [R4: option_fml > option_fml > $o,A4: option_fml] :
% 4.36/2.18 ? [X3: option_fml] :
% 4.36/2.18 ( ( A4 = X3 )
% 4.36/2.18 & ! [Y3: option_fml] :
% 4.36/2.18 ( ( R4 @ Y3 @ X3 )
% 4.36/2.18 => ( accp_option_fml @ R4 @ Y3 ) ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_200_accp_Ointros,axiom,
% 4.36/2.18 ! [R3: produc1024976764on_trm > produc1024976764on_trm > $o,X2: produc1024976764on_trm] :
% 4.36/2.18 ( ! [Y4: produc1024976764on_trm] :
% 4.36/2.18 ( ( R3 @ Y4 @ X2 )
% 4.36/2.18 => ( accp_P394694195on_trm @ R3 @ Y4 ) )
% 4.36/2.18 => ( accp_P394694195on_trm @ R3 @ X2 ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_201_accp_Ointros,axiom,
% 4.36/2.18 ! [R3: produc1072747943on_trm > produc1072747943on_trm > $o,X2: produc1072747943on_trm] :
% 4.36/2.18 ( ! [Y4: produc1072747943on_trm] :
% 4.36/2.18 ( ( R3 @ Y4 @ X2 )
% 4.36/2.18 => ( accp_P758790320on_trm @ R3 @ Y4 ) )
% 4.36/2.18 => ( accp_P758790320on_trm @ R3 @ X2 ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_202_accp_Ointros,axiom,
% 4.36/2.18 ! [R3: produc464795408on_trm > produc464795408on_trm > $o,X2: produc464795408on_trm] :
% 4.36/2.18 ( ! [Y4: produc464795408on_trm] :
% 4.36/2.18 ( ( R3 @ Y4 @ X2 )
% 4.36/2.18 => ( accp_P419951815on_trm @ R3 @ Y4 ) )
% 4.36/2.18 => ( accp_P419951815on_trm @ R3 @ X2 ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_203_accp_Ointros,axiom,
% 4.36/2.18 ! [R3: option_trm > option_trm > $o,X2: option_trm] :
% 4.36/2.18 ( ! [Y4: option_trm] :
% 4.36/2.18 ( ( R3 @ Y4 @ X2 )
% 4.36/2.18 => ( accp_option_trm @ R3 @ Y4 ) )
% 4.36/2.18 => ( accp_option_trm @ R3 @ X2 ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_204_accp_Ointros,axiom,
% 4.36/2.18 ! [R3: option_fml > option_fml > $o,X2: option_fml] :
% 4.36/2.18 ( ! [Y4: option_fml] :
% 4.36/2.18 ( ( R3 @ Y4 @ X2 )
% 4.36/2.18 => ( accp_option_fml @ R3 @ Y4 ) )
% 4.36/2.18 => ( accp_option_fml @ R3 @ X2 ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_205_accp__induct,axiom,
% 4.36/2.18 ! [R3: produc1024976764on_trm > produc1024976764on_trm > $o,A3: produc1024976764on_trm,P: produc1024976764on_trm > $o] :
% 4.36/2.18 ( ( accp_P394694195on_trm @ R3 @ A3 )
% 4.36/2.18 => ( ! [X: produc1024976764on_trm] :
% 4.36/2.18 ( ( accp_P394694195on_trm @ R3 @ X )
% 4.36/2.18 => ( ! [Y5: produc1024976764on_trm] :
% 4.36/2.18 ( ( R3 @ Y5 @ X )
% 4.36/2.18 => ( P @ Y5 ) )
% 4.36/2.18 => ( P @ X ) ) )
% 4.36/2.18 => ( P @ A3 ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_206_accp__induct,axiom,
% 4.36/2.18 ! [R3: produc1072747943on_trm > produc1072747943on_trm > $o,A3: produc1072747943on_trm,P: produc1072747943on_trm > $o] :
% 4.36/2.18 ( ( accp_P758790320on_trm @ R3 @ A3 )
% 4.36/2.18 => ( ! [X: produc1072747943on_trm] :
% 4.36/2.18 ( ( accp_P758790320on_trm @ R3 @ X )
% 4.36/2.18 => ( ! [Y5: produc1072747943on_trm] :
% 4.36/2.18 ( ( R3 @ Y5 @ X )
% 4.36/2.18 => ( P @ Y5 ) )
% 4.36/2.18 => ( P @ X ) ) )
% 4.36/2.18 => ( P @ A3 ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_207_accp__induct,axiom,
% 4.36/2.18 ! [R3: produc464795408on_trm > produc464795408on_trm > $o,A3: produc464795408on_trm,P: produc464795408on_trm > $o] :
% 4.36/2.18 ( ( accp_P419951815on_trm @ R3 @ A3 )
% 4.36/2.18 => ( ! [X: produc464795408on_trm] :
% 4.36/2.18 ( ( accp_P419951815on_trm @ R3 @ X )
% 4.36/2.18 => ( ! [Y5: produc464795408on_trm] :
% 4.36/2.18 ( ( R3 @ Y5 @ X )
% 4.36/2.18 => ( P @ Y5 ) )
% 4.36/2.18 => ( P @ X ) ) )
% 4.36/2.18 => ( P @ A3 ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_208_accp__induct,axiom,
% 4.36/2.18 ! [R3: option_trm > option_trm > $o,A3: option_trm,P: option_trm > $o] :
% 4.36/2.18 ( ( accp_option_trm @ R3 @ A3 )
% 4.36/2.18 => ( ! [X: option_trm] :
% 4.36/2.18 ( ( accp_option_trm @ R3 @ X )
% 4.36/2.18 => ( ! [Y5: option_trm] :
% 4.36/2.18 ( ( R3 @ Y5 @ X )
% 4.36/2.18 => ( P @ Y5 ) )
% 4.36/2.18 => ( P @ X ) ) )
% 4.36/2.18 => ( P @ A3 ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_209_accp__induct,axiom,
% 4.36/2.18 ! [R3: option_fml > option_fml > $o,A3: option_fml,P: option_fml > $o] :
% 4.36/2.18 ( ( accp_option_fml @ R3 @ A3 )
% 4.36/2.18 => ( ! [X: option_fml] :
% 4.36/2.18 ( ( accp_option_fml @ R3 @ X )
% 4.36/2.18 => ( ! [Y5: option_fml] :
% 4.36/2.18 ( ( R3 @ Y5 @ X )
% 4.36/2.18 => ( P @ Y5 ) )
% 4.36/2.18 => ( P @ X ) ) )
% 4.36/2.18 => ( P @ A3 ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_210_accp_Oinducts,axiom,
% 4.36/2.18 ! [R3: produc1024976764on_trm > produc1024976764on_trm > $o,X2: produc1024976764on_trm,P: produc1024976764on_trm > $o] :
% 4.36/2.18 ( ( accp_P394694195on_trm @ R3 @ X2 )
% 4.36/2.18 => ( ! [X: produc1024976764on_trm] :
% 4.36/2.18 ( ! [Y5: produc1024976764on_trm] :
% 4.36/2.18 ( ( R3 @ Y5 @ X )
% 4.36/2.18 => ( accp_P394694195on_trm @ R3 @ Y5 ) )
% 4.36/2.18 => ( ! [Y5: produc1024976764on_trm] :
% 4.36/2.18 ( ( R3 @ Y5 @ X )
% 4.36/2.18 => ( P @ Y5 ) )
% 4.36/2.18 => ( P @ X ) ) )
% 4.36/2.18 => ( P @ X2 ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_211_accp_Oinducts,axiom,
% 4.36/2.18 ! [R3: produc1072747943on_trm > produc1072747943on_trm > $o,X2: produc1072747943on_trm,P: produc1072747943on_trm > $o] :
% 4.36/2.18 ( ( accp_P758790320on_trm @ R3 @ X2 )
% 4.36/2.18 => ( ! [X: produc1072747943on_trm] :
% 4.36/2.18 ( ! [Y5: produc1072747943on_trm] :
% 4.36/2.18 ( ( R3 @ Y5 @ X )
% 4.36/2.18 => ( accp_P758790320on_trm @ R3 @ Y5 ) )
% 4.36/2.18 => ( ! [Y5: produc1072747943on_trm] :
% 4.36/2.18 ( ( R3 @ Y5 @ X )
% 4.36/2.18 => ( P @ Y5 ) )
% 4.36/2.18 => ( P @ X ) ) )
% 4.36/2.18 => ( P @ X2 ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_212_accp_Oinducts,axiom,
% 4.36/2.18 ! [R3: produc464795408on_trm > produc464795408on_trm > $o,X2: produc464795408on_trm,P: produc464795408on_trm > $o] :
% 4.36/2.18 ( ( accp_P419951815on_trm @ R3 @ X2 )
% 4.36/2.18 => ( ! [X: produc464795408on_trm] :
% 4.36/2.18 ( ! [Y5: produc464795408on_trm] :
% 4.36/2.18 ( ( R3 @ Y5 @ X )
% 4.36/2.18 => ( accp_P419951815on_trm @ R3 @ Y5 ) )
% 4.36/2.18 => ( ! [Y5: produc464795408on_trm] :
% 4.36/2.18 ( ( R3 @ Y5 @ X )
% 4.36/2.18 => ( P @ Y5 ) )
% 4.36/2.18 => ( P @ X ) ) )
% 4.36/2.18 => ( P @ X2 ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_213_accp_Oinducts,axiom,
% 4.36/2.18 ! [R3: option_trm > option_trm > $o,X2: option_trm,P: option_trm > $o] :
% 4.36/2.18 ( ( accp_option_trm @ R3 @ X2 )
% 4.36/2.18 => ( ! [X: option_trm] :
% 4.36/2.18 ( ! [Y5: option_trm] :
% 4.36/2.18 ( ( R3 @ Y5 @ X )
% 4.36/2.18 => ( accp_option_trm @ R3 @ Y5 ) )
% 4.36/2.18 => ( ! [Y5: option_trm] :
% 4.36/2.18 ( ( R3 @ Y5 @ X )
% 4.36/2.18 => ( P @ Y5 ) )
% 4.36/2.18 => ( P @ X ) ) )
% 4.36/2.18 => ( P @ X2 ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_214_accp_Oinducts,axiom,
% 4.36/2.18 ! [R3: option_fml > option_fml > $o,X2: option_fml,P: option_fml > $o] :
% 4.36/2.18 ( ( accp_option_fml @ R3 @ X2 )
% 4.36/2.18 => ( ! [X: option_fml] :
% 4.36/2.18 ( ! [Y5: option_fml] :
% 4.36/2.18 ( ( R3 @ Y5 @ X )
% 4.36/2.18 => ( accp_option_fml @ R3 @ Y5 ) )
% 4.36/2.18 => ( ! [Y5: option_fml] :
% 4.36/2.18 ( ( R3 @ Y5 @ X )
% 4.36/2.18 => ( P @ Y5 ) )
% 4.36/2.18 => ( P @ X ) ) )
% 4.36/2.18 => ( P @ X2 ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_215_accp__downward,axiom,
% 4.36/2.18 ! [R3: produc1024976764on_trm > produc1024976764on_trm > $o,B3: produc1024976764on_trm,A3: produc1024976764on_trm] :
% 4.36/2.18 ( ( accp_P394694195on_trm @ R3 @ B3 )
% 4.36/2.18 => ( ( R3 @ A3 @ B3 )
% 4.36/2.18 => ( accp_P394694195on_trm @ R3 @ A3 ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_216_accp__downward,axiom,
% 4.36/2.18 ! [R3: produc1072747943on_trm > produc1072747943on_trm > $o,B3: produc1072747943on_trm,A3: produc1072747943on_trm] :
% 4.36/2.18 ( ( accp_P758790320on_trm @ R3 @ B3 )
% 4.36/2.18 => ( ( R3 @ A3 @ B3 )
% 4.36/2.18 => ( accp_P758790320on_trm @ R3 @ A3 ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_217_accp__downward,axiom,
% 4.36/2.18 ! [R3: produc464795408on_trm > produc464795408on_trm > $o,B3: produc464795408on_trm,A3: produc464795408on_trm] :
% 4.36/2.18 ( ( accp_P419951815on_trm @ R3 @ B3 )
% 4.36/2.18 => ( ( R3 @ A3 @ B3 )
% 4.36/2.18 => ( accp_P419951815on_trm @ R3 @ A3 ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_218_accp__downward,axiom,
% 4.36/2.18 ! [R3: option_trm > option_trm > $o,B3: option_trm,A3: option_trm] :
% 4.36/2.18 ( ( accp_option_trm @ R3 @ B3 )
% 4.36/2.18 => ( ( R3 @ A3 @ B3 )
% 4.36/2.18 => ( accp_option_trm @ R3 @ A3 ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_219_accp__downward,axiom,
% 4.36/2.18 ! [R3: option_fml > option_fml > $o,B3: option_fml,A3: option_fml] :
% 4.36/2.18 ( ( accp_option_fml @ R3 @ B3 )
% 4.36/2.18 => ( ( R3 @ A3 @ B3 )
% 4.36/2.18 => ( accp_option_fml @ R3 @ A3 ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_220_not__accp__down,axiom,
% 4.36/2.18 ! [R: produc1024976764on_trm > produc1024976764on_trm > $o,X2: produc1024976764on_trm] :
% 4.36/2.18 ( ~ ( accp_P394694195on_trm @ R @ X2 )
% 4.36/2.18 => ~ ! [Z4: produc1024976764on_trm] :
% 4.36/2.18 ( ( R @ Z4 @ X2 )
% 4.36/2.18 => ( accp_P394694195on_trm @ R @ Z4 ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_221_not__accp__down,axiom,
% 4.36/2.18 ! [R: produc1072747943on_trm > produc1072747943on_trm > $o,X2: produc1072747943on_trm] :
% 4.36/2.18 ( ~ ( accp_P758790320on_trm @ R @ X2 )
% 4.36/2.18 => ~ ! [Z4: produc1072747943on_trm] :
% 4.36/2.18 ( ( R @ Z4 @ X2 )
% 4.36/2.18 => ( accp_P758790320on_trm @ R @ Z4 ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_222_not__accp__down,axiom,
% 4.36/2.18 ! [R: produc464795408on_trm > produc464795408on_trm > $o,X2: produc464795408on_trm] :
% 4.36/2.18 ( ~ ( accp_P419951815on_trm @ R @ X2 )
% 4.36/2.18 => ~ ! [Z4: produc464795408on_trm] :
% 4.36/2.18 ( ( R @ Z4 @ X2 )
% 4.36/2.18 => ( accp_P419951815on_trm @ R @ Z4 ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_223_not__accp__down,axiom,
% 4.36/2.18 ! [R: option_trm > option_trm > $o,X2: option_trm] :
% 4.36/2.18 ( ~ ( accp_option_trm @ R @ X2 )
% 4.36/2.18 => ~ ! [Z4: option_trm] :
% 4.36/2.18 ( ( R @ Z4 @ X2 )
% 4.36/2.18 => ( accp_option_trm @ R @ Z4 ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_224_not__accp__down,axiom,
% 4.36/2.18 ! [R: option_fml > option_fml > $o,X2: option_fml] :
% 4.36/2.18 ( ~ ( accp_option_fml @ R @ X2 )
% 4.36/2.18 => ~ ! [Z4: option_fml] :
% 4.36/2.18 ( ( R @ Z4 @ X2 )
% 4.36/2.18 => ( accp_option_fml @ R @ Z4 ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_225_accp__induct__rule,axiom,
% 4.36/2.18 ! [R3: produc1024976764on_trm > produc1024976764on_trm > $o,A3: produc1024976764on_trm,P: produc1024976764on_trm > $o] :
% 4.36/2.18 ( ( accp_P394694195on_trm @ R3 @ A3 )
% 4.36/2.18 => ( ! [X: produc1024976764on_trm] :
% 4.36/2.18 ( ( accp_P394694195on_trm @ R3 @ X )
% 4.36/2.18 => ( ! [Y5: produc1024976764on_trm] :
% 4.36/2.18 ( ( R3 @ Y5 @ X )
% 4.36/2.18 => ( P @ Y5 ) )
% 4.36/2.18 => ( P @ X ) ) )
% 4.36/2.18 => ( P @ A3 ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_226_accp__induct__rule,axiom,
% 4.36/2.18 ! [R3: produc1072747943on_trm > produc1072747943on_trm > $o,A3: produc1072747943on_trm,P: produc1072747943on_trm > $o] :
% 4.36/2.18 ( ( accp_P758790320on_trm @ R3 @ A3 )
% 4.36/2.18 => ( ! [X: produc1072747943on_trm] :
% 4.36/2.18 ( ( accp_P758790320on_trm @ R3 @ X )
% 4.36/2.18 => ( ! [Y5: produc1072747943on_trm] :
% 4.36/2.18 ( ( R3 @ Y5 @ X )
% 4.36/2.18 => ( P @ Y5 ) )
% 4.36/2.18 => ( P @ X ) ) )
% 4.36/2.18 => ( P @ A3 ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_227_accp__induct__rule,axiom,
% 4.36/2.18 ! [R3: produc464795408on_trm > produc464795408on_trm > $o,A3: produc464795408on_trm,P: produc464795408on_trm > $o] :
% 4.36/2.18 ( ( accp_P419951815on_trm @ R3 @ A3 )
% 4.36/2.18 => ( ! [X: produc464795408on_trm] :
% 4.36/2.18 ( ( accp_P419951815on_trm @ R3 @ X )
% 4.36/2.18 => ( ! [Y5: produc464795408on_trm] :
% 4.36/2.18 ( ( R3 @ Y5 @ X )
% 4.36/2.18 => ( P @ Y5 ) )
% 4.36/2.18 => ( P @ X ) ) )
% 4.36/2.18 => ( P @ A3 ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_228_accp__induct__rule,axiom,
% 4.36/2.18 ! [R3: option_trm > option_trm > $o,A3: option_trm,P: option_trm > $o] :
% 4.36/2.18 ( ( accp_option_trm @ R3 @ A3 )
% 4.36/2.18 => ( ! [X: option_trm] :
% 4.36/2.18 ( ( accp_option_trm @ R3 @ X )
% 4.36/2.18 => ( ! [Y5: option_trm] :
% 4.36/2.18 ( ( R3 @ Y5 @ X )
% 4.36/2.18 => ( P @ Y5 ) )
% 4.36/2.18 => ( P @ X ) ) )
% 4.36/2.18 => ( P @ A3 ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_229_accp__induct__rule,axiom,
% 4.36/2.18 ! [R3: option_fml > option_fml > $o,A3: option_fml,P: option_fml > $o] :
% 4.36/2.18 ( ( accp_option_fml @ R3 @ A3 )
% 4.36/2.18 => ( ! [X: option_fml] :
% 4.36/2.18 ( ( accp_option_fml @ R3 @ X )
% 4.36/2.18 => ( ! [Y5: option_fml] :
% 4.36/2.18 ( ( R3 @ Y5 @ X )
% 4.36/2.18 => ( P @ Y5 ) )
% 4.36/2.18 => ( P @ X ) ) )
% 4.36/2.18 => ( P @ A3 ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_230_Geqo_Opelims,axiom,
% 4.36/2.18 ! [X2: option_trm,Xa: option_trm,Y2: option_fml] :
% 4.36/2.18 ( ( ( uSubst152838031e_Geqo @ X2 @ Xa )
% 4.36/2.18 = Y2 )
% 4.36/2.18 => ( ( accp_P758790320on_trm @ uSubst1304144938qo_rel @ ( produc709594775on_trm @ X2 @ Xa ) )
% 4.36/2.18 => ( ! [Theta2: trm] :
% 4.36/2.18 ( ( X2
% 4.36/2.18 = ( some_trm @ Theta2 ) )
% 4.36/2.18 => ! [Eta2: trm] :
% 4.36/2.18 ( ( Xa
% 4.36/2.18 = ( some_trm @ Eta2 ) )
% 4.36/2.18 => ( ( Y2
% 4.36/2.18 = ( some_fml @ ( geq @ Theta2 @ Eta2 ) ) )
% 4.36/2.18 => ~ ( accp_P758790320on_trm @ uSubst1304144938qo_rel @ ( produc709594775on_trm @ ( some_trm @ Theta2 ) @ ( some_trm @ Eta2 ) ) ) ) ) )
% 4.36/2.18 => ( ( ( X2 = none_trm )
% 4.36/2.18 => ( ( Y2 = none_fml )
% 4.36/2.18 => ~ ( accp_P758790320on_trm @ uSubst1304144938qo_rel @ ( produc709594775on_trm @ none_trm @ Xa ) ) ) )
% 4.36/2.18 => ~ ! [V2: trm] :
% 4.36/2.18 ( ( X2
% 4.36/2.18 = ( some_trm @ V2 ) )
% 4.36/2.18 => ( ( Xa = none_trm )
% 4.36/2.18 => ( ( Y2 = none_fml )
% 4.36/2.18 => ~ ( accp_P758790320on_trm @ uSubst1304144938qo_rel @ ( produc709594775on_trm @ ( some_trm @ V2 ) @ none_trm ) ) ) ) ) ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_231_Diamondo_Ocases,axiom,
% 4.36/2.18 ! [X2: produc1739631244on_fml] :
% 4.36/2.18 ( ! [Alpha: game,Phi2: fml] :
% 4.36/2.18 ( X2
% 4.36/2.18 != ( produc2124676926on_fml @ ( some_game @ Alpha ) @ ( some_fml @ Phi2 ) ) )
% 4.36/2.18 => ( ! [Phi2: option_fml] :
% 4.36/2.18 ( X2
% 4.36/2.18 != ( produc2124676926on_fml @ none_game @ Phi2 ) )
% 4.36/2.18 => ~ ! [V2: game] :
% 4.36/2.18 ( X2
% 4.36/2.18 != ( produc2124676926on_fml @ ( some_game @ V2 ) @ none_fml ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_232_subrelI,axiom,
% 4.36/2.18 ! [R3: set_Pr622314946on_fml,S2: set_Pr622314946on_fml] :
% 4.36/2.18 ( ! [X: option_game,Y4: option_fml] :
% 4.36/2.18 ( ( member1883102883on_fml @ ( produc2124676926on_fml @ X @ Y4 ) @ R3 )
% 4.36/2.18 => ( member1883102883on_fml @ ( produc2124676926on_fml @ X @ Y4 ) @ S2 ) )
% 4.36/2.18 => ( ord_le782333474on_fml @ R3 @ S2 ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_233_subrelI,axiom,
% 4.36/2.18 ! [R3: set_Pr1471344007on_trm,S2: set_Pr1471344007on_trm] :
% 4.36/2.18 ( ! [X: option_trm,Y4: option_trm] :
% 4.36/2.18 ( ( member165817296on_trm @ ( produc709594775on_trm @ X @ Y4 ) @ R3 )
% 4.36/2.18 => ( member165817296on_trm @ ( produc709594775on_trm @ X @ Y4 ) @ S2 ) )
% 4.36/2.18 => ( ord_le1322722599on_trm @ R3 @ S2 ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_234_subrelI,axiom,
% 4.36/2.18 ! [R3: set_Pr927595527on_fml,S2: set_Pr927595527on_fml] :
% 4.36/2.18 ( ! [X: option_fml,Y4: option_fml] :
% 4.36/2.18 ( ( member1287158352on_fml @ ( produc909629463on_fml @ X @ Y4 ) @ R3 )
% 4.36/2.18 => ( member1287158352on_fml @ ( produc909629463on_fml @ X @ Y4 ) @ S2 ) )
% 4.36/2.18 => ( ord_le778974119on_fml @ R3 @ S2 ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_235_subrelI,axiom,
% 4.36/2.18 ! [R3: set_Pr943832262on_trm,S2: set_Pr943832262on_trm] :
% 4.36/2.18 ( ! [X: char,Y4: option_trm] :
% 4.36/2.18 ( ( member694524327on_trm @ ( produc1500300866on_trm @ X @ Y4 ) @ R3 )
% 4.36/2.18 => ( member694524327on_trm @ ( produc1500300866on_trm @ X @ Y4 ) @ S2 ) )
% 4.36/2.18 => ( ord_le541293862on_trm @ R3 @ S2 ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_236_subrelI,axiom,
% 4.36/2.18 ! [R3: set_Pr1235432374le_trm,S2: set_Pr1235432374le_trm] :
% 4.36/2.18 ( ! [X: set_variable,Y4: trm] :
% 4.36/2.18 ( ( member2122665623le_trm @ ( produc1482344242le_trm @ X @ Y4 ) @ R3 )
% 4.36/2.18 => ( member2122665623le_trm @ ( produc1482344242le_trm @ X @ Y4 ) @ S2 ) )
% 4.36/2.18 => ( ord_le2102862870le_trm @ R3 @ S2 ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_237_ssubst__Pair__rhs,axiom,
% 4.36/2.18 ! [R3: option_game,S2: option_fml,R: set_Pr622314946on_fml,S3: option_fml] :
% 4.36/2.18 ( ( member1883102883on_fml @ ( produc2124676926on_fml @ R3 @ S2 ) @ R )
% 4.36/2.18 => ( ( S3 = S2 )
% 4.36/2.18 => ( member1883102883on_fml @ ( produc2124676926on_fml @ R3 @ S3 ) @ R ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_238_ssubst__Pair__rhs,axiom,
% 4.36/2.18 ! [R3: option_trm,S2: option_trm,R: set_Pr1471344007on_trm,S3: option_trm] :
% 4.36/2.18 ( ( member165817296on_trm @ ( produc709594775on_trm @ R3 @ S2 ) @ R )
% 4.36/2.18 => ( ( S3 = S2 )
% 4.36/2.18 => ( member165817296on_trm @ ( produc709594775on_trm @ R3 @ S3 ) @ R ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_239_ssubst__Pair__rhs,axiom,
% 4.36/2.18 ! [R3: option_fml,S2: option_fml,R: set_Pr927595527on_fml,S3: option_fml] :
% 4.36/2.18 ( ( member1287158352on_fml @ ( produc909629463on_fml @ R3 @ S2 ) @ R )
% 4.36/2.18 => ( ( S3 = S2 )
% 4.36/2.18 => ( member1287158352on_fml @ ( produc909629463on_fml @ R3 @ S3 ) @ R ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_240_ssubst__Pair__rhs,axiom,
% 4.36/2.18 ! [R3: char,S2: option_trm,R: set_Pr943832262on_trm,S3: option_trm] :
% 4.36/2.18 ( ( member694524327on_trm @ ( produc1500300866on_trm @ R3 @ S2 ) @ R )
% 4.36/2.18 => ( ( S3 = S2 )
% 4.36/2.18 => ( member694524327on_trm @ ( produc1500300866on_trm @ R3 @ S3 ) @ R ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_241_ssubst__Pair__rhs,axiom,
% 4.36/2.18 ! [R3: set_variable,S2: trm,R: set_Pr1235432374le_trm,S3: trm] :
% 4.36/2.18 ( ( member2122665623le_trm @ ( produc1482344242le_trm @ R3 @ S2 ) @ R )
% 4.36/2.18 => ( ( S3 = S2 )
% 4.36/2.18 => ( member2122665623le_trm @ ( produc1482344242le_trm @ R3 @ S3 ) @ R ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_242_pred__equals__eq2,axiom,
% 4.36/2.18 ! [R: set_Pr622314946on_fml,S: set_Pr622314946on_fml] :
% 4.36/2.18 ( ( ( ^ [X3: option_game,Y3: option_fml] : ( member1883102883on_fml @ ( produc2124676926on_fml @ X3 @ Y3 ) @ R ) )
% 4.36/2.18 = ( ^ [X3: option_game,Y3: option_fml] : ( member1883102883on_fml @ ( produc2124676926on_fml @ X3 @ Y3 ) @ S ) ) )
% 4.36/2.18 = ( R = S ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_243_pred__equals__eq2,axiom,
% 4.36/2.18 ! [R: set_Pr1471344007on_trm,S: set_Pr1471344007on_trm] :
% 4.36/2.18 ( ( ( ^ [X3: option_trm,Y3: option_trm] : ( member165817296on_trm @ ( produc709594775on_trm @ X3 @ Y3 ) @ R ) )
% 4.36/2.18 = ( ^ [X3: option_trm,Y3: option_trm] : ( member165817296on_trm @ ( produc709594775on_trm @ X3 @ Y3 ) @ S ) ) )
% 4.36/2.18 = ( R = S ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_244_pred__equals__eq2,axiom,
% 4.36/2.18 ! [R: set_Pr927595527on_fml,S: set_Pr927595527on_fml] :
% 4.36/2.18 ( ( ( ^ [X3: option_fml,Y3: option_fml] : ( member1287158352on_fml @ ( produc909629463on_fml @ X3 @ Y3 ) @ R ) )
% 4.36/2.18 = ( ^ [X3: option_fml,Y3: option_fml] : ( member1287158352on_fml @ ( produc909629463on_fml @ X3 @ Y3 ) @ S ) ) )
% 4.36/2.18 = ( R = S ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_245_pred__equals__eq2,axiom,
% 4.36/2.18 ! [R: set_Pr943832262on_trm,S: set_Pr943832262on_trm] :
% 4.36/2.18 ( ( ( ^ [X3: char,Y3: option_trm] : ( member694524327on_trm @ ( produc1500300866on_trm @ X3 @ Y3 ) @ R ) )
% 4.36/2.18 = ( ^ [X3: char,Y3: option_trm] : ( member694524327on_trm @ ( produc1500300866on_trm @ X3 @ Y3 ) @ S ) ) )
% 4.36/2.18 = ( R = S ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_246_pred__equals__eq2,axiom,
% 4.36/2.18 ! [R: set_Pr1235432374le_trm,S: set_Pr1235432374le_trm] :
% 4.36/2.18 ( ( ( ^ [X3: set_variable,Y3: trm] : ( member2122665623le_trm @ ( produc1482344242le_trm @ X3 @ Y3 ) @ R ) )
% 4.36/2.18 = ( ^ [X3: set_variable,Y3: trm] : ( member2122665623le_trm @ ( produc1482344242le_trm @ X3 @ Y3 ) @ S ) ) )
% 4.36/2.18 = ( R = S ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_247_pred__subset__eq2,axiom,
% 4.36/2.18 ! [R: set_Pr622314946on_fml,S: set_Pr622314946on_fml] :
% 4.36/2.18 ( ( ord_le1588489637_fml_o
% 4.36/2.18 @ ^ [X3: option_game,Y3: option_fml] : ( member1883102883on_fml @ ( produc2124676926on_fml @ X3 @ Y3 ) @ R )
% 4.36/2.18 @ ^ [X3: option_game,Y3: option_fml] : ( member1883102883on_fml @ ( produc2124676926on_fml @ X3 @ Y3 ) @ S ) )
% 4.36/2.18 = ( ord_le782333474on_fml @ R @ S ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_248_pred__subset__eq2,axiom,
% 4.36/2.18 ! [R: set_Pr1471344007on_trm,S: set_Pr1471344007on_trm] :
% 4.36/2.18 ( ( ord_le847028878_trm_o
% 4.36/2.18 @ ^ [X3: option_trm,Y3: option_trm] : ( member165817296on_trm @ ( produc709594775on_trm @ X3 @ Y3 ) @ R )
% 4.36/2.18 @ ^ [X3: option_trm,Y3: option_trm] : ( member165817296on_trm @ ( produc709594775on_trm @ X3 @ Y3 ) @ S ) )
% 4.36/2.18 = ( ord_le1322722599on_trm @ R @ S ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_249_pred__subset__eq2,axiom,
% 4.36/2.18 ! [R: set_Pr927595527on_fml,S: set_Pr927595527on_fml] :
% 4.36/2.18 ( ( ord_le802833166_fml_o
% 4.36/2.18 @ ^ [X3: option_fml,Y3: option_fml] : ( member1287158352on_fml @ ( produc909629463on_fml @ X3 @ Y3 ) @ R )
% 4.36/2.18 @ ^ [X3: option_fml,Y3: option_fml] : ( member1287158352on_fml @ ( produc909629463on_fml @ X3 @ Y3 ) @ S ) )
% 4.36/2.18 = ( ord_le778974119on_fml @ R @ S ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_250_pred__subset__eq2,axiom,
% 4.36/2.18 ! [R: set_Pr943832262on_trm,S: set_Pr943832262on_trm] :
% 4.36/2.18 ( ( ord_le1890124833_trm_o
% 4.36/2.18 @ ^ [X3: char,Y3: option_trm] : ( member694524327on_trm @ ( produc1500300866on_trm @ X3 @ Y3 ) @ R )
% 4.36/2.18 @ ^ [X3: char,Y3: option_trm] : ( member694524327on_trm @ ( produc1500300866on_trm @ X3 @ Y3 ) @ S ) )
% 4.36/2.18 = ( ord_le541293862on_trm @ R @ S ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_251_pred__subset__eq2,axiom,
% 4.36/2.18 ! [R: set_Pr1235432374le_trm,S: set_Pr1235432374le_trm] :
% 4.36/2.18 ( ( ord_le691957041_trm_o
% 4.36/2.18 @ ^ [X3: set_variable,Y3: trm] : ( member2122665623le_trm @ ( produc1482344242le_trm @ X3 @ Y3 ) @ R )
% 4.36/2.18 @ ^ [X3: set_variable,Y3: trm] : ( member2122665623le_trm @ ( produc1482344242le_trm @ X3 @ Y3 ) @ S ) )
% 4.36/2.18 = ( ord_le2102862870le_trm @ R @ S ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_252_option_Odisc__eq__case_I1_J,axiom,
% 4.36/2.18 ! [Option: option_trm] :
% 4.36/2.18 ( ( Option = none_trm )
% 4.36/2.18 = ( case_option_o_trm @ $true
% 4.36/2.18 @ ^ [Uu: trm] : $false
% 4.36/2.18 @ Option ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_253_option_Odisc__eq__case_I1_J,axiom,
% 4.36/2.18 ! [Option: option_fml] :
% 4.36/2.18 ( ( Option = none_fml )
% 4.36/2.18 = ( case_option_o_fml @ $true
% 4.36/2.18 @ ^ [Uu: fml] : $false
% 4.36/2.18 @ Option ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_254_option_Odisc__eq__case_I1_J,axiom,
% 4.36/2.18 ! [Option: option_game] :
% 4.36/2.18 ( ( Option = none_game )
% 4.36/2.18 = ( case_option_o_game @ $true
% 4.36/2.18 @ ^ [Uu: game] : $false
% 4.36/2.18 @ Option ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_255_option_Odisc__eq__case_I2_J,axiom,
% 4.36/2.18 ! [Option: option_trm] :
% 4.36/2.18 ( ( Option != none_trm )
% 4.36/2.18 = ( case_option_o_trm @ $false
% 4.36/2.18 @ ^ [Uu: trm] : $true
% 4.36/2.18 @ Option ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_256_option_Odisc__eq__case_I2_J,axiom,
% 4.36/2.18 ! [Option: option_fml] :
% 4.36/2.18 ( ( Option != none_fml )
% 4.36/2.18 = ( case_option_o_fml @ $false
% 4.36/2.18 @ ^ [Uu: fml] : $true
% 4.36/2.18 @ Option ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_257_option_Odisc__eq__case_I2_J,axiom,
% 4.36/2.18 ! [Option: option_game] :
% 4.36/2.18 ( ( Option != none_game )
% 4.36/2.18 = ( case_option_o_game @ $false
% 4.36/2.18 @ ^ [Uu: game] : $true
% 4.36/2.18 @ Option ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_258_Timeso_Ocases,axiom,
% 4.36/2.18 ! [X2: produc1072747943on_trm] :
% 4.36/2.18 ( ! [Theta2: trm,Eta2: trm] :
% 4.36/2.18 ( X2
% 4.36/2.18 != ( produc709594775on_trm @ ( some_trm @ Theta2 ) @ ( some_trm @ Eta2 ) ) )
% 4.36/2.18 => ( ! [Eta2: option_trm] :
% 4.36/2.18 ( X2
% 4.36/2.18 != ( produc709594775on_trm @ none_trm @ Eta2 ) )
% 4.36/2.18 => ~ ! [V2: trm] :
% 4.36/2.18 ( X2
% 4.36/2.18 != ( produc709594775on_trm @ ( some_trm @ V2 ) @ none_trm ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_259_case__optionE,axiom,
% 4.36/2.18 ! [P: $o,Q: trm > $o,X2: option_trm] :
% 4.36/2.18 ( ( case_option_o_trm @ P @ Q @ X2 )
% 4.36/2.18 => ( ( ( X2 = none_trm )
% 4.36/2.18 => ~ P )
% 4.36/2.18 => ~ ! [Y4: trm] :
% 4.36/2.18 ( ( X2
% 4.36/2.18 = ( some_trm @ Y4 ) )
% 4.36/2.18 => ~ ( Q @ Y4 ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_260_case__optionE,axiom,
% 4.36/2.18 ! [P: $o,Q: fml > $o,X2: option_fml] :
% 4.36/2.18 ( ( case_option_o_fml @ P @ Q @ X2 )
% 4.36/2.18 => ( ( ( X2 = none_fml )
% 4.36/2.18 => ~ P )
% 4.36/2.18 => ~ ! [Y4: fml] :
% 4.36/2.18 ( ( X2
% 4.36/2.18 = ( some_fml @ Y4 ) )
% 4.36/2.18 => ~ ( Q @ Y4 ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_261_case__optionE,axiom,
% 4.36/2.18 ! [P: $o,Q: game > $o,X2: option_game] :
% 4.36/2.18 ( ( case_option_o_game @ P @ Q @ X2 )
% 4.36/2.18 => ( ( ( X2 = none_game )
% 4.36/2.18 => ~ P )
% 4.36/2.18 => ~ ! [Y4: game] :
% 4.36/2.18 ( ( X2
% 4.36/2.18 = ( some_game @ Y4 ) )
% 4.36/2.18 => ~ ( Q @ Y4 ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_262_Timeso_Opelims,axiom,
% 4.36/2.18 ! [X2: option_trm,Xa: option_trm,Y2: option_trm] :
% 4.36/2.18 ( ( ( uSubst918876924Timeso @ X2 @ Xa )
% 4.36/2.18 = Y2 )
% 4.36/2.18 => ( ( accp_P758790320on_trm @ uSubst924844285so_rel @ ( produc709594775on_trm @ X2 @ Xa ) )
% 4.36/2.18 => ( ! [Theta2: trm] :
% 4.36/2.18 ( ( X2
% 4.36/2.18 = ( some_trm @ Theta2 ) )
% 4.36/2.18 => ! [Eta2: trm] :
% 4.36/2.18 ( ( Xa
% 4.36/2.18 = ( some_trm @ Eta2 ) )
% 4.36/2.18 => ( ( Y2
% 4.36/2.18 = ( some_trm @ ( times @ Theta2 @ Eta2 ) ) )
% 4.36/2.18 => ~ ( accp_P758790320on_trm @ uSubst924844285so_rel @ ( produc709594775on_trm @ ( some_trm @ Theta2 ) @ ( some_trm @ Eta2 ) ) ) ) ) )
% 4.36/2.18 => ( ( ( X2 = none_trm )
% 4.36/2.18 => ( ( Y2 = none_trm )
% 4.36/2.18 => ~ ( accp_P758790320on_trm @ uSubst924844285so_rel @ ( produc709594775on_trm @ none_trm @ Xa ) ) ) )
% 4.36/2.18 => ~ ! [V2: trm] :
% 4.36/2.18 ( ( X2
% 4.36/2.18 = ( some_trm @ V2 ) )
% 4.36/2.18 => ( ( Xa = none_trm )
% 4.36/2.18 => ( ( Y2 = none_trm )
% 4.36/2.18 => ~ ( accp_P758790320on_trm @ uSubst924844285so_rel @ ( produc709594775on_trm @ ( some_trm @ V2 ) @ none_trm ) ) ) ) ) ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_263_Pluso_Opelims,axiom,
% 4.36/2.18 ! [X2: option_trm,Xa: option_trm,Y2: option_trm] :
% 4.36/2.18 ( ( ( uSubst141955042_Pluso @ X2 @ Xa )
% 4.36/2.18 = Y2 )
% 4.36/2.18 => ( ( accp_P758790320on_trm @ uSubst691094423so_rel @ ( produc709594775on_trm @ X2 @ Xa ) )
% 4.36/2.18 => ( ! [Theta2: trm] :
% 4.36/2.18 ( ( X2
% 4.36/2.18 = ( some_trm @ Theta2 ) )
% 4.36/2.18 => ! [Eta2: trm] :
% 4.36/2.18 ( ( Xa
% 4.36/2.18 = ( some_trm @ Eta2 ) )
% 4.36/2.18 => ( ( Y2
% 4.36/2.18 = ( some_trm @ ( plus @ Theta2 @ Eta2 ) ) )
% 4.36/2.18 => ~ ( accp_P758790320on_trm @ uSubst691094423so_rel @ ( produc709594775on_trm @ ( some_trm @ Theta2 ) @ ( some_trm @ Eta2 ) ) ) ) ) )
% 4.36/2.18 => ( ( ( X2 = none_trm )
% 4.36/2.18 => ( ( Y2 = none_trm )
% 4.36/2.18 => ~ ( accp_P758790320on_trm @ uSubst691094423so_rel @ ( produc709594775on_trm @ none_trm @ Xa ) ) ) )
% 4.36/2.18 => ~ ! [V2: trm] :
% 4.36/2.18 ( ( X2
% 4.36/2.18 = ( some_trm @ V2 ) )
% 4.36/2.18 => ( ( Xa = none_trm )
% 4.36/2.18 => ( ( Y2 = none_trm )
% 4.36/2.18 => ~ ( accp_P758790320on_trm @ uSubst691094423so_rel @ ( produc709594775on_trm @ ( some_trm @ V2 ) @ none_trm ) ) ) ) ) ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_264_ODEo_Ocases,axiom,
% 4.36/2.18 ! [X2: produc464795408on_trm] :
% 4.36/2.18 ( ! [X: char,Theta2: trm] :
% 4.36/2.18 ( X2
% 4.36/2.18 != ( produc1500300866on_trm @ X @ ( some_trm @ Theta2 ) ) )
% 4.36/2.18 => ~ ! [X: char] :
% 4.36/2.18 ( X2
% 4.36/2.18 != ( produc1500300866on_trm @ X @ none_trm ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_265_Assigno_Ocases,axiom,
% 4.36/2.18 ! [X2: produc1024976764on_trm] :
% 4.36/2.18 ( ! [X: variable,Theta2: trm] :
% 4.36/2.18 ( X2
% 4.36/2.18 != ( produc1743721902on_trm @ X @ ( some_trm @ Theta2 ) ) )
% 4.36/2.18 => ~ ! [X: variable] :
% 4.36/2.18 ( X2
% 4.36/2.18 != ( produc1743721902on_trm @ X @ none_trm ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_266_Composeo_Ocases,axiom,
% 4.36/2.18 ! [X2: produc1016592119n_game] :
% 4.36/2.18 ( ! [Alpha: game,Beta: game] :
% 4.36/2.18 ( X2
% 4.36/2.18 != ( produc1111617711n_game @ ( some_game @ Alpha ) @ ( some_game @ Beta ) ) )
% 4.36/2.18 => ( ! [Alpha: option_game] :
% 4.36/2.18 ( X2
% 4.36/2.18 != ( produc1111617711n_game @ Alpha @ none_game ) )
% 4.36/2.18 => ~ ! [V2: game] :
% 4.36/2.18 ( X2
% 4.36/2.18 != ( produc1111617711n_game @ none_game @ ( some_game @ V2 ) ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_267_Existso_Ocases,axiom,
% 4.36/2.18 ! [X2: produc1408538418on_fml] :
% 4.36/2.18 ( ! [X: variable,Phi2: fml] :
% 4.36/2.18 ( X2
% 4.36/2.18 != ( produc1205977188on_fml @ X @ ( some_fml @ Phi2 ) ) )
% 4.36/2.18 => ~ ! [X: variable] :
% 4.36/2.18 ( X2
% 4.36/2.18 != ( produc1205977188on_fml @ X @ none_fml ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_268_Ando_Ocases,axiom,
% 4.36/2.18 ! [X2: produc46605351on_fml] :
% 4.36/2.18 ( ! [Phi2: fml,Psi: fml] :
% 4.36/2.18 ( X2
% 4.36/2.18 != ( produc909629463on_fml @ ( some_fml @ Phi2 ) @ ( some_fml @ Psi ) ) )
% 4.36/2.18 => ( ! [Psi: option_fml] :
% 4.36/2.18 ( X2
% 4.36/2.18 != ( produc909629463on_fml @ none_fml @ Psi ) )
% 4.36/2.18 => ~ ! [V2: fml] :
% 4.36/2.18 ( X2
% 4.36/2.18 != ( produc909629463on_fml @ ( some_fml @ V2 ) @ none_fml ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_269_usubstappt_Opsimps_I7_J,axiom,
% 4.36/2.18 ! [Sigma: produc1418842292n_game,U: set_variable,Theta: trm] :
% 4.36/2.18 ( ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ Sigma @ ( produc1482344242le_trm @ U @ ( differential @ Theta ) ) ) )
% 4.36/2.18 => ( ( uSubst516392818stappt @ Sigma @ U @ ( differential @ Theta ) )
% 4.36/2.18 = ( uSubst716837505ntialo
% 4.36/2.18 @ ( uSubst516392818stappt @ Sigma
% 4.36/2.18 @ ( collect_variable
% 4.36/2.18 @ ^ [X3: variable] : $true )
% 4.36/2.18 @ Theta ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_270_usubstappt_Opsimps_I6_J,axiom,
% 4.36/2.18 ! [Sigma: produc1418842292n_game,U: set_variable,Theta: trm,Eta: trm] :
% 4.36/2.18 ( ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ Sigma @ ( produc1482344242le_trm @ U @ ( times @ Theta @ Eta ) ) ) )
% 4.36/2.18 => ( ( uSubst516392818stappt @ Sigma @ U @ ( times @ Theta @ Eta ) )
% 4.36/2.18 = ( uSubst918876924Timeso @ ( uSubst516392818stappt @ Sigma @ U @ Theta ) @ ( uSubst516392818stappt @ Sigma @ U @ Eta ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_271_usubstappt_Opsimps_I5_J,axiom,
% 4.36/2.18 ! [Sigma: produc1418842292n_game,U: set_variable,Theta: trm,Eta: trm] :
% 4.36/2.18 ( ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ Sigma @ ( produc1482344242le_trm @ U @ ( plus @ Theta @ Eta ) ) ) )
% 4.36/2.18 => ( ( uSubst516392818stappt @ Sigma @ U @ ( plus @ Theta @ Eta ) )
% 4.36/2.18 = ( uSubst141955042_Pluso @ ( uSubst516392818stappt @ Sigma @ U @ Theta ) @ ( uSubst516392818stappt @ Sigma @ U @ Eta ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_272_usubstappt_Opsimps_I1_J,axiom,
% 4.36/2.18 ! [Sigma: produc1418842292n_game,U: set_variable,X2: variable] :
% 4.36/2.18 ( ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ Sigma @ ( produc1482344242le_trm @ U @ ( var @ X2 ) ) ) )
% 4.36/2.18 => ( ( uSubst516392818stappt @ Sigma @ U @ ( var @ X2 ) )
% 4.36/2.18 = ( some_trm @ ( var @ X2 ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_273_usubstappt_Opsimps_I2_J,axiom,
% 4.36/2.18 ! [Sigma: produc1418842292n_game,U: set_variable,R3: real] :
% 4.36/2.18 ( ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ Sigma @ ( produc1482344242le_trm @ U @ ( number @ R3 ) ) ) )
% 4.36/2.18 => ( ( uSubst516392818stappt @ Sigma @ U @ ( number @ R3 ) )
% 4.36/2.18 = ( some_trm @ ( number @ R3 ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_274_in__lex__prod,axiom,
% 4.36/2.18 ! [A3: option_trm,B3: option_fml,A6: option_trm,B6: option_fml,R3: set_Pr1471344007on_trm,S2: set_Pr927595527on_fml] :
% 4.36/2.18 ( ( member1316917136on_fml @ ( produc1235825367on_fml @ ( produc171850061on_fml @ A3 @ B3 ) @ ( produc171850061on_fml @ A6 @ B6 ) ) @ ( lex_pr1724583269on_fml @ R3 @ S2 ) )
% 4.36/2.18 = ( ( member165817296on_trm @ ( produc709594775on_trm @ A3 @ A6 ) @ R3 )
% 4.36/2.18 | ( ( A3 = A6 )
% 4.36/2.18 & ( member1287158352on_fml @ ( produc909629463on_fml @ B3 @ B6 ) @ S2 ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_275_in__lex__prod,axiom,
% 4.36/2.18 ! [A3: option_fml,B3: option_trm,A6: option_fml,B6: option_trm,R3: set_Pr927595527on_fml,S2: set_Pr1471344007on_trm] :
% 4.36/2.18 ( ( member1883874960on_trm @ ( produc2132972503on_trm @ ( produc1447374177on_trm @ A3 @ B3 ) @ ( produc1447374177on_trm @ A6 @ B6 ) ) @ ( lex_pr852623737on_trm @ R3 @ S2 ) )
% 4.36/2.18 = ( ( member1287158352on_fml @ ( produc909629463on_fml @ A3 @ A6 ) @ R3 )
% 4.36/2.18 | ( ( A3 = A6 )
% 4.36/2.18 & ( member165817296on_trm @ ( produc709594775on_trm @ B3 @ B6 ) @ S2 ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_276_in__lex__prod,axiom,
% 4.36/2.18 ! [A3: option_game,B3: option_fml,A6: option_game,B6: option_fml,R3: set_Pr1625152599n_game,S2: set_Pr927595527on_fml] :
% 4.36/2.18 ( ( member113767842on_fml @ ( produc556056113on_fml @ ( produc2124676926on_fml @ A3 @ B3 ) @ ( produc2124676926on_fml @ A6 @ B6 ) ) @ ( lex_pr425996582on_fml @ R3 @ S2 ) )
% 4.36/2.18 = ( ( member191809696n_game @ ( produc1111617711n_game @ A3 @ A6 ) @ R3 )
% 4.36/2.18 | ( ( A3 = A6 )
% 4.36/2.18 & ( member1287158352on_fml @ ( produc909629463on_fml @ B3 @ B6 ) @ S2 ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_277_in__lex__prod,axiom,
% 4.36/2.18 ! [A3: option_trm,B3: option_trm,A6: option_trm,B6: option_trm,R3: set_Pr1471344007on_trm,S2: set_Pr1471344007on_trm] :
% 4.36/2.18 ( ( member602811152on_trm @ ( produc2001752919on_trm @ ( produc709594775on_trm @ A3 @ B3 ) @ ( produc709594775on_trm @ A6 @ B6 ) ) @ ( lex_pr114844335on_trm @ R3 @ S2 ) )
% 4.36/2.18 = ( ( member165817296on_trm @ ( produc709594775on_trm @ A3 @ A6 ) @ R3 )
% 4.36/2.18 | ( ( A3 = A6 )
% 4.36/2.18 & ( member165817296on_trm @ ( produc709594775on_trm @ B3 @ B6 ) @ S2 ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_278_in__lex__prod,axiom,
% 4.36/2.18 ! [A3: option_fml,B3: option_fml,A6: option_fml,B6: option_fml,R3: set_Pr927595527on_fml,S2: set_Pr927595527on_fml] :
% 4.36/2.18 ( ( member450497296on_fml @ ( produc1367044951on_fml @ ( produc909629463on_fml @ A3 @ B3 ) @ ( produc909629463on_fml @ A6 @ B6 ) ) @ ( lex_pr314879023on_fml @ R3 @ S2 ) )
% 4.36/2.18 = ( ( member1287158352on_fml @ ( produc909629463on_fml @ A3 @ A6 ) @ R3 )
% 4.36/2.18 | ( ( A3 = A6 )
% 4.36/2.18 & ( member1287158352on_fml @ ( produc909629463on_fml @ B3 @ B6 ) @ S2 ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_279_in__lex__prod,axiom,
% 4.36/2.18 ! [A3: char,B3: option_trm,A6: char,B6: option_trm,R3: set_Pr604539619r_char,S2: set_Pr1471344007on_trm] :
% 4.36/2.18 ( ( member1950256170on_trm @ ( produc444919481on_trm @ ( produc1500300866on_trm @ A3 @ B3 ) @ ( produc1500300866on_trm @ A6 @ B6 ) ) @ ( lex_pr1901327402on_trm @ R3 @ S2 ) )
% 4.36/2.18 = ( ( member1866856748r_char @ ( produc19545147r_char @ A3 @ A6 ) @ R3 )
% 4.36/2.18 | ( ( A3 = A6 )
% 4.36/2.18 & ( member165817296on_trm @ ( produc709594775on_trm @ B3 @ B6 ) @ S2 ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_280_in__lex__prod,axiom,
% 4.36/2.18 ! [A3: set_variable,B3: trm,A6: set_variable,B6: trm,R3: set_Pr181266295riable,S2: set_Pr491793543rm_trm] :
% 4.36/2.18 ( ( member1150310282le_trm @ ( produc1056455193le_trm @ ( produc1482344242le_trm @ A3 @ B3 ) @ ( produc1482344242le_trm @ A6 @ B6 ) ) @ ( lex_pr1522821402le_trm @ R3 @ S2 ) )
% 4.36/2.18 = ( ( member1978718144riable @ ( produc1766592463riable @ A3 @ A6 ) @ R3 )
% 4.36/2.18 | ( ( A3 = A6 )
% 4.36/2.18 & ( member1735386832rm_trm @ ( product_Pair_trm_trm @ B3 @ B6 ) @ S2 ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_281_trm_Oinject_I2_J,axiom,
% 4.36/2.18 ! [X23: real,Y23: real] :
% 4.36/2.18 ( ( ( number @ X23 )
% 4.36/2.18 = ( number @ Y23 ) )
% 4.36/2.18 = ( X23 = Y23 ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_282_trm_Oinject_I1_J,axiom,
% 4.36/2.18 ! [X1: variable,Y1: variable] :
% 4.36/2.18 ( ( ( var @ X1 )
% 4.36/2.18 = ( var @ Y1 ) )
% 4.36/2.18 = ( X1 = Y1 ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_283_trm_Odistinct_I17_J,axiom,
% 4.36/2.18 ! [X23: real,X51: trm,X52: trm] :
% 4.36/2.18 ( ( number @ X23 )
% 4.36/2.18 != ( plus @ X51 @ X52 ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_284_trm_Odistinct_I19_J,axiom,
% 4.36/2.18 ! [X23: real,X61: trm,X62: trm] :
% 4.36/2.18 ( ( number @ X23 )
% 4.36/2.18 != ( times @ X61 @ X62 ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_285_trm_Odistinct_I21_J,axiom,
% 4.36/2.18 ! [X23: real,X7: trm] :
% 4.36/2.18 ( ( number @ X23 )
% 4.36/2.18 != ( differential @ X7 ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_286_trm_Odistinct_I7_J,axiom,
% 4.36/2.18 ! [X1: variable,X51: trm,X52: trm] :
% 4.36/2.18 ( ( var @ X1 )
% 4.36/2.18 != ( plus @ X51 @ X52 ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_287_trm_Odistinct_I9_J,axiom,
% 4.36/2.18 ! [X1: variable,X61: trm,X62: trm] :
% 4.36/2.18 ( ( var @ X1 )
% 4.36/2.18 != ( times @ X61 @ X62 ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_288_trm_Odistinct_I11_J,axiom,
% 4.36/2.18 ! [X1: variable,X7: trm] :
% 4.36/2.18 ( ( var @ X1 )
% 4.36/2.18 != ( differential @ X7 ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_289_trm_Odistinct_I1_J,axiom,
% 4.36/2.18 ! [X1: variable,X23: real] :
% 4.36/2.18 ( ( var @ X1 )
% 4.36/2.18 != ( number @ X23 ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_290_usubstappt_Osimps_I2_J,axiom,
% 4.36/2.18 ! [Sigma: produc1418842292n_game,U: set_variable,R3: real] :
% 4.36/2.18 ( ( uSubst516392818stappt @ Sigma @ U @ ( number @ R3 ) )
% 4.36/2.18 = ( some_trm @ ( number @ R3 ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_291_usubstappt_Osimps_I1_J,axiom,
% 4.36/2.18 ! [Sigma: produc1418842292n_game,U: set_variable,X2: variable] :
% 4.36/2.18 ( ( uSubst516392818stappt @ Sigma @ U @ ( var @ X2 ) )
% 4.36/2.18 = ( some_trm @ ( var @ X2 ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_292_usubstappt_Ocases,axiom,
% 4.36/2.18 ! [X2: produc1699626005le_trm] :
% 4.36/2.18 ( ! [Sigma2: produc1418842292n_game,U3: set_variable,X: variable] :
% 4.36/2.18 ( X2
% 4.36/2.18 != ( produc2015636557le_trm @ Sigma2 @ ( produc1482344242le_trm @ U3 @ ( var @ X ) ) ) )
% 4.36/2.18 => ( ! [Sigma2: produc1418842292n_game,U3: set_variable,R5: real] :
% 4.36/2.18 ( X2
% 4.36/2.18 != ( produc2015636557le_trm @ Sigma2 @ ( produc1482344242le_trm @ U3 @ ( number @ R5 ) ) ) )
% 4.36/2.18 => ( ! [Sigma2: produc1418842292n_game,U3: set_variable,F3: char] :
% 4.36/2.18 ( X2
% 4.36/2.18 != ( produc2015636557le_trm @ Sigma2 @ ( produc1482344242le_trm @ U3 @ ( const @ F3 ) ) ) )
% 4.36/2.18 => ( ! [Sigma2: produc1418842292n_game,U3: set_variable,F3: char,Theta2: trm] :
% 4.36/2.18 ( X2
% 4.36/2.18 != ( produc2015636557le_trm @ Sigma2 @ ( produc1482344242le_trm @ U3 @ ( func @ F3 @ Theta2 ) ) ) )
% 4.36/2.18 => ( ! [Sigma2: produc1418842292n_game,U3: set_variable,Theta2: trm,Eta2: trm] :
% 4.36/2.18 ( X2
% 4.36/2.18 != ( produc2015636557le_trm @ Sigma2 @ ( produc1482344242le_trm @ U3 @ ( plus @ Theta2 @ Eta2 ) ) ) )
% 4.36/2.18 => ( ! [Sigma2: produc1418842292n_game,U3: set_variable,Theta2: trm,Eta2: trm] :
% 4.36/2.18 ( X2
% 4.36/2.18 != ( produc2015636557le_trm @ Sigma2 @ ( produc1482344242le_trm @ U3 @ ( times @ Theta2 @ Eta2 ) ) ) )
% 4.36/2.18 => ~ ! [Sigma2: produc1418842292n_game,U3: set_variable,Theta2: trm] :
% 4.36/2.18 ( X2
% 4.36/2.18 != ( produc2015636557le_trm @ Sigma2 @ ( produc1482344242le_trm @ U3 @ ( differential @ Theta2 ) ) ) ) ) ) ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_293_Testo_Osimps_I2_J,axiom,
% 4.36/2.18 ( ( uSubst1367128042_Testo @ none_fml )
% 4.36/2.18 = none_game ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_294_Testo__undef,axiom,
% 4.36/2.18 ! [Phi: option_fml] :
% 4.36/2.18 ( ( ( uSubst1367128042_Testo @ Phi )
% 4.36/2.18 = none_game )
% 4.36/2.18 = ( Phi = none_fml ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_295_trm_Oinject_I4_J,axiom,
% 4.36/2.18 ! [X41: char,X42: trm,Y41: char,Y42: trm] :
% 4.36/2.18 ( ( ( func @ X41 @ X42 )
% 4.36/2.18 = ( func @ Y41 @ Y42 ) )
% 4.36/2.18 = ( ( X41 = Y41 )
% 4.36/2.18 & ( X42 = Y42 ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_296_trm_Oinject_I3_J,axiom,
% 4.36/2.18 ! [X32: char,Y32: char] :
% 4.36/2.18 ( ( ( const @ X32 )
% 4.36/2.18 = ( const @ Y32 ) )
% 4.36/2.18 = ( X32 = Y32 ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_297_trm_Odistinct_I3_J,axiom,
% 4.36/2.18 ! [X1: variable,X32: char] :
% 4.36/2.18 ( ( var @ X1 )
% 4.36/2.18 != ( const @ X32 ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_298_trm_Odistinct_I5_J,axiom,
% 4.36/2.18 ! [X1: variable,X41: char,X42: trm] :
% 4.36/2.18 ( ( var @ X1 )
% 4.36/2.18 != ( func @ X41 @ X42 ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_299_trm_Odistinct_I13_J,axiom,
% 4.36/2.18 ! [X23: real,X32: char] :
% 4.36/2.18 ( ( number @ X23 )
% 4.36/2.18 != ( const @ X32 ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_300_trm_Odistinct_I15_J,axiom,
% 4.36/2.18 ! [X23: real,X41: char,X42: trm] :
% 4.36/2.18 ( ( number @ X23 )
% 4.36/2.18 != ( func @ X41 @ X42 ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_301_trm_Odistinct_I23_J,axiom,
% 4.36/2.18 ! [X32: char,X41: char,X42: trm] :
% 4.36/2.18 ( ( const @ X32 )
% 4.36/2.18 != ( func @ X41 @ X42 ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_302_trm_Odistinct_I29_J,axiom,
% 4.36/2.18 ! [X32: char,X7: trm] :
% 4.36/2.18 ( ( const @ X32 )
% 4.36/2.18 != ( differential @ X7 ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_303_trm_Odistinct_I27_J,axiom,
% 4.36/2.18 ! [X32: char,X61: trm,X62: trm] :
% 4.36/2.18 ( ( const @ X32 )
% 4.36/2.18 != ( times @ X61 @ X62 ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_304_trm_Odistinct_I25_J,axiom,
% 4.36/2.18 ! [X32: char,X51: trm,X52: trm] :
% 4.36/2.18 ( ( const @ X32 )
% 4.36/2.18 != ( plus @ X51 @ X52 ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_305_trm_Odistinct_I35_J,axiom,
% 4.36/2.18 ! [X41: char,X42: trm,X7: trm] :
% 4.36/2.18 ( ( func @ X41 @ X42 )
% 4.36/2.18 != ( differential @ X7 ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_306_trm_Odistinct_I33_J,axiom,
% 4.36/2.18 ! [X41: char,X42: trm,X61: trm,X62: trm] :
% 4.36/2.18 ( ( func @ X41 @ X42 )
% 4.36/2.18 != ( times @ X61 @ X62 ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_307_trm_Odistinct_I31_J,axiom,
% 4.36/2.18 ! [X41: char,X42: trm,X51: trm,X52: trm] :
% 4.36/2.18 ( ( func @ X41 @ X42 )
% 4.36/2.18 != ( plus @ X51 @ X52 ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_308_trm_Oinduct,axiom,
% 4.36/2.18 ! [P: trm > $o,Trm: trm] :
% 4.36/2.18 ( ! [X: variable] : ( P @ ( var @ X ) )
% 4.36/2.18 => ( ! [X: real] : ( P @ ( number @ X ) )
% 4.36/2.18 => ( ! [X: char] : ( P @ ( const @ X ) )
% 4.36/2.18 => ( ! [X1a: char,X2a: trm] :
% 4.36/2.18 ( ( P @ X2a )
% 4.36/2.18 => ( P @ ( func @ X1a @ X2a ) ) )
% 4.36/2.18 => ( ! [X1a: trm,X2a: trm] :
% 4.36/2.18 ( ( P @ X1a )
% 4.36/2.18 => ( ( P @ X2a )
% 4.36/2.18 => ( P @ ( plus @ X1a @ X2a ) ) ) )
% 4.36/2.18 => ( ! [X1a: trm,X2a: trm] :
% 4.36/2.18 ( ( P @ X1a )
% 4.36/2.18 => ( ( P @ X2a )
% 4.36/2.18 => ( P @ ( times @ X1a @ X2a ) ) ) )
% 4.36/2.18 => ( ! [X: trm] :
% 4.36/2.18 ( ( P @ X )
% 4.36/2.18 => ( P @ ( differential @ X ) ) )
% 4.36/2.18 => ( P @ Trm ) ) ) ) ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_309_trm_Oexhaust,axiom,
% 4.36/2.18 ! [Y2: trm] :
% 4.36/2.18 ( ! [X12: variable] :
% 4.36/2.18 ( Y2
% 4.36/2.18 != ( var @ X12 ) )
% 4.36/2.18 => ( ! [X24: real] :
% 4.36/2.18 ( Y2
% 4.36/2.18 != ( number @ X24 ) )
% 4.36/2.18 => ( ! [X33: char] :
% 4.36/2.18 ( Y2
% 4.36/2.18 != ( const @ X33 ) )
% 4.36/2.18 => ( ! [X412: char,X422: trm] :
% 4.36/2.18 ( Y2
% 4.36/2.18 != ( func @ X412 @ X422 ) )
% 4.36/2.18 => ( ! [X512: trm,X522: trm] :
% 4.36/2.18 ( Y2
% 4.36/2.18 != ( plus @ X512 @ X522 ) )
% 4.36/2.18 => ( ! [X612: trm,X622: trm] :
% 4.36/2.18 ( Y2
% 4.36/2.18 != ( times @ X612 @ X622 ) )
% 4.36/2.18 => ~ ! [X72: trm] :
% 4.36/2.18 ( Y2
% 4.36/2.18 != ( differential @ X72 ) ) ) ) ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_310_term__sem_Ocases,axiom,
% 4.36/2.18 ! [X2: produc833882726rp_trm] :
% 4.36/2.18 ( ! [I2: denotational_interp,X: variable] :
% 4.36/2.18 ( X2
% 4.36/2.18 != ( produc1132922070rp_trm @ I2 @ ( var @ X ) ) )
% 4.36/2.18 => ( ! [I2: denotational_interp,R5: real] :
% 4.36/2.18 ( X2
% 4.36/2.18 != ( produc1132922070rp_trm @ I2 @ ( number @ R5 ) ) )
% 4.36/2.18 => ( ! [I2: denotational_interp,F3: char] :
% 4.36/2.18 ( X2
% 4.36/2.18 != ( produc1132922070rp_trm @ I2 @ ( const @ F3 ) ) )
% 4.36/2.18 => ( ! [I2: denotational_interp,F3: char,Theta2: trm] :
% 4.36/2.18 ( X2
% 4.36/2.18 != ( produc1132922070rp_trm @ I2 @ ( func @ F3 @ Theta2 ) ) )
% 4.36/2.18 => ( ! [I2: denotational_interp,Theta2: trm,Eta2: trm] :
% 4.36/2.18 ( X2
% 4.36/2.18 != ( produc1132922070rp_trm @ I2 @ ( plus @ Theta2 @ Eta2 ) ) )
% 4.36/2.18 => ( ! [I2: denotational_interp,Theta2: trm,Eta2: trm] :
% 4.36/2.18 ( X2
% 4.36/2.18 != ( produc1132922070rp_trm @ I2 @ ( times @ Theta2 @ Eta2 ) ) )
% 4.36/2.18 => ~ ! [I2: denotational_interp,Theta2: trm] :
% 4.36/2.18 ( X2
% 4.36/2.18 != ( produc1132922070rp_trm @ I2 @ ( differential @ Theta2 ) ) ) ) ) ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_311_usubstappt_Opsimps_I3_J,axiom,
% 4.36/2.18 ! [Sigma: produc1418842292n_game,U: set_variable,F: char] :
% 4.36/2.18 ( ( accp_P1877119646le_trm @ uSubst1917534215pt_rel @ ( produc2015636557le_trm @ Sigma @ ( produc1482344242le_trm @ U @ ( const @ F ) ) ) )
% 4.36/2.18 => ( ( uSubst516392818stappt @ Sigma @ U @ ( const @ F ) )
% 4.36/2.18 = ( uSubst1559070963pconst @ Sigma @ U @ F ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_312_term__sem_Oinduct,axiom,
% 4.36/2.18 ! [P: denotational_interp > trm > $o,A0: denotational_interp,A1: trm] :
% 4.36/2.18 ( ! [I2: denotational_interp,X: variable] : ( P @ I2 @ ( var @ X ) )
% 4.36/2.18 => ( ! [I2: denotational_interp,R5: real] : ( P @ I2 @ ( number @ R5 ) )
% 4.36/2.18 => ( ! [I2: denotational_interp,F3: char] : ( P @ I2 @ ( const @ F3 ) )
% 4.36/2.18 => ( ! [I2: denotational_interp,F3: char,Theta2: trm] :
% 4.36/2.18 ( ( P @ I2 @ Theta2 )
% 4.36/2.18 => ( P @ I2 @ ( func @ F3 @ Theta2 ) ) )
% 4.36/2.18 => ( ! [I2: denotational_interp,Theta2: trm] :
% 4.36/2.18 ( ( P @ I2 @ Theta2 )
% 4.36/2.18 => ! [Eta2: trm] :
% 4.36/2.18 ( ( P @ I2 @ Eta2 )
% 4.36/2.18 => ( P @ I2 @ ( plus @ Theta2 @ Eta2 ) ) ) )
% 4.36/2.18 => ( ! [I2: denotational_interp,Theta2: trm] :
% 4.36/2.18 ( ( P @ I2 @ Theta2 )
% 4.36/2.18 => ! [Eta2: trm] :
% 4.36/2.18 ( ( P @ I2 @ Eta2 )
% 4.36/2.18 => ( P @ I2 @ ( times @ Theta2 @ Eta2 ) ) ) )
% 4.36/2.18 => ( ! [I2: denotational_interp,Theta2: trm] :
% 4.36/2.18 ( ( ? [Xa2: char] :
% 4.36/2.18 ( member_char @ Xa2
% 4.36/2.18 @ ( collect_char
% 4.36/2.18 @ ^ [Uu: char] : $true ) )
% 4.36/2.18 => ( P @ I2 @ Theta2 ) )
% 4.36/2.18 => ( P @ I2 @ ( differential @ Theta2 ) ) )
% 4.36/2.18 => ( P @ A0 @ A1 ) ) ) ) ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_313_usubstappt_Osimps_I3_J,axiom,
% 4.36/2.18 ! [Sigma: produc1418842292n_game,U: set_variable,F: char] :
% 4.36/2.18 ( ( uSubst516392818stappt @ Sigma @ U @ ( const @ F ) )
% 4.36/2.18 = ( uSubst1559070963pconst @ Sigma @ U @ F ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_314_image2__def,axiom,
% 4.36/2.18 ( bNF_Gr2142503190on_fml
% 4.36/2.18 = ( ^ [A2: set_variable,F2: variable > option_game,G: variable > option_fml] :
% 4.36/2.18 ( collec749447393on_fml
% 4.36/2.18 @ ^ [Uu: produc1739631244on_fml] :
% 4.36/2.18 ? [A4: variable] :
% 4.36/2.18 ( ( Uu
% 4.36/2.18 = ( produc2124676926on_fml @ ( F2 @ A4 ) @ ( G @ A4 ) ) )
% 4.36/2.18 & ( member_variable @ A4 @ A2 ) ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_315_image2__def,axiom,
% 4.36/2.18 ( bNF_Gr756940202on_fml
% 4.36/2.18 = ( ^ [A2: set_char,F2: char > option_game,G: char > option_fml] :
% 4.36/2.18 ( collec749447393on_fml
% 4.36/2.18 @ ^ [Uu: produc1739631244on_fml] :
% 4.36/2.18 ? [A4: char] :
% 4.36/2.18 ( ( Uu
% 4.36/2.18 = ( produc2124676926on_fml @ ( F2 @ A4 ) @ ( G @ A4 ) ) )
% 4.36/2.18 & ( member_char @ A4 @ A2 ) ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_316_image2__def,axiom,
% 4.36/2.18 ( bNF_Gr400922303on_trm
% 4.36/2.18 = ( ^ [A2: set_variable,F2: variable > option_trm,G: variable > option_trm] :
% 4.36/2.18 ( collec1697116690on_trm
% 4.36/2.18 @ ^ [Uu: produc1072747943on_trm] :
% 4.36/2.18 ? [A4: variable] :
% 4.36/2.18 ( ( Uu
% 4.36/2.18 = ( produc709594775on_trm @ ( F2 @ A4 ) @ ( G @ A4 ) ) )
% 4.36/2.18 & ( member_variable @ A4 @ A2 ) ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_317_image2__def,axiom,
% 4.36/2.18 ( bNF_Gr1666135339on_trm
% 4.36/2.18 = ( ^ [A2: set_char,F2: char > option_trm,G: char > option_trm] :
% 4.36/2.18 ( collec1697116690on_trm
% 4.36/2.18 @ ^ [Uu: produc1072747943on_trm] :
% 4.36/2.18 ? [A4: char] :
% 4.36/2.18 ( ( Uu
% 4.36/2.18 = ( produc709594775on_trm @ ( F2 @ A4 ) @ ( G @ A4 ) ) )
% 4.36/2.18 & ( member_char @ A4 @ A2 ) ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_318_image2__def,axiom,
% 4.36/2.18 ( bNF_Gr600956991on_fml
% 4.36/2.18 = ( ^ [A2: set_variable,F2: variable > option_fml,G: variable > option_fml] :
% 4.36/2.18 ( collec670974098on_fml
% 4.36/2.18 @ ^ [Uu: produc46605351on_fml] :
% 4.36/2.18 ? [A4: variable] :
% 4.36/2.18 ( ( Uu
% 4.36/2.18 = ( produc909629463on_fml @ ( F2 @ A4 ) @ ( G @ A4 ) ) )
% 4.36/2.18 & ( member_variable @ A4 @ A2 ) ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_319_image2__def,axiom,
% 4.36/2.18 ( bNF_Gr1866170027on_fml
% 4.36/2.18 = ( ^ [A2: set_char,F2: char > option_fml,G: char > option_fml] :
% 4.36/2.18 ( collec670974098on_fml
% 4.36/2.18 @ ^ [Uu: produc46605351on_fml] :
% 4.36/2.18 ? [A4: char] :
% 4.36/2.18 ( ( Uu
% 4.36/2.18 = ( produc909629463on_fml @ ( F2 @ A4 ) @ ( G @ A4 ) ) )
% 4.36/2.18 & ( member_char @ A4 @ A2 ) ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_320_image2__def,axiom,
% 4.36/2.18 ( bNF_Gr1933470746on_trm
% 4.36/2.18 = ( ^ [A2: set_variable,F2: variable > char,G: variable > option_trm] :
% 4.36/2.18 ( collec1756633317on_trm
% 4.36/2.18 @ ^ [Uu: produc464795408on_trm] :
% 4.36/2.18 ? [A4: variable] :
% 4.36/2.18 ( ( Uu
% 4.36/2.18 = ( produc1500300866on_trm @ ( F2 @ A4 ) @ ( G @ A4 ) ) )
% 4.36/2.18 & ( member_variable @ A4 @ A2 ) ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_321_image2__def,axiom,
% 4.36/2.18 ( bNF_Gr951178926on_trm
% 4.36/2.18 = ( ^ [A2: set_char,F2: char > char,G: char > option_trm] :
% 4.36/2.18 ( collec1756633317on_trm
% 4.36/2.18 @ ^ [Uu: produc464795408on_trm] :
% 4.36/2.18 ? [A4: char] :
% 4.36/2.18 ( ( Uu
% 4.36/2.18 = ( produc1500300866on_trm @ ( F2 @ A4 ) @ ( G @ A4 ) ) )
% 4.36/2.18 & ( member_char @ A4 @ A2 ) ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_322_image2__def,axiom,
% 4.36/2.18 ( bNF_Gr1330108682le_trm
% 4.36/2.18 = ( ^ [A2: set_variable,F2: variable > set_variable,G: variable > trm] :
% 4.36/2.18 ( collec575343829le_trm
% 4.36/2.18 @ ^ [Uu: produc1367888000le_trm] :
% 4.36/2.18 ? [A4: variable] :
% 4.36/2.18 ( ( Uu
% 4.36/2.18 = ( produc1482344242le_trm @ ( F2 @ A4 ) @ ( G @ A4 ) ) )
% 4.36/2.18 & ( member_variable @ A4 @ A2 ) ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_323_image2__def,axiom,
% 4.36/2.18 ( bNF_Gr852774302le_trm
% 4.36/2.18 = ( ^ [A2: set_char,F2: char > set_variable,G: char > trm] :
% 4.36/2.18 ( collec575343829le_trm
% 4.36/2.18 @ ^ [Uu: produc1367888000le_trm] :
% 4.36/2.18 ? [A4: char] :
% 4.36/2.18 ( ( Uu
% 4.36/2.18 = ( produc1482344242le_trm @ ( F2 @ A4 ) @ ( G @ A4 ) ) )
% 4.36/2.18 & ( member_char @ A4 @ A2 ) ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_324_Testo_Oelims,axiom,
% 4.36/2.18 ! [X2: option_fml,Y2: option_game] :
% 4.36/2.18 ( ( ( uSubst1367128042_Testo @ X2 )
% 4.36/2.18 = Y2 )
% 4.36/2.18 => ( ! [Phi2: fml] :
% 4.36/2.18 ( ( X2
% 4.36/2.18 = ( some_fml @ Phi2 ) )
% 4.36/2.18 => ( Y2
% 4.36/2.18 != ( some_game @ ( test @ Phi2 ) ) ) )
% 4.36/2.18 => ~ ( ( X2 = none_fml )
% 4.36/2.18 => ( Y2 != none_game ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_325_game_Oinject_I3_J,axiom,
% 4.36/2.18 ! [X32: fml,Y32: fml] :
% 4.36/2.18 ( ( ( test @ X32 )
% 4.36/2.18 = ( test @ Y32 ) )
% 4.36/2.18 = ( X32 = Y32 ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_326_image2__eqI,axiom,
% 4.36/2.18 ! [B3: option_game,F: variable > option_game,X2: variable,C: option_fml,G2: variable > option_fml,A: set_variable] :
% 4.36/2.18 ( ( B3
% 4.36/2.18 = ( F @ X2 ) )
% 4.36/2.18 => ( ( C
% 4.36/2.18 = ( G2 @ X2 ) )
% 4.36/2.18 => ( ( member_variable @ X2 @ A )
% 4.36/2.18 => ( member1883102883on_fml @ ( produc2124676926on_fml @ B3 @ C ) @ ( bNF_Gr2142503190on_fml @ A @ F @ G2 ) ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_327_image2__eqI,axiom,
% 4.36/2.18 ! [B3: option_game,F: char > option_game,X2: char,C: option_fml,G2: char > option_fml,A: set_char] :
% 4.36/2.18 ( ( B3
% 4.36/2.18 = ( F @ X2 ) )
% 4.36/2.18 => ( ( C
% 4.36/2.18 = ( G2 @ X2 ) )
% 4.36/2.18 => ( ( member_char @ X2 @ A )
% 4.36/2.18 => ( member1883102883on_fml @ ( produc2124676926on_fml @ B3 @ C ) @ ( bNF_Gr756940202on_fml @ A @ F @ G2 ) ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_328_image2__eqI,axiom,
% 4.36/2.18 ! [B3: option_trm,F: variable > option_trm,X2: variable,C: option_trm,G2: variable > option_trm,A: set_variable] :
% 4.36/2.18 ( ( B3
% 4.36/2.18 = ( F @ X2 ) )
% 4.36/2.18 => ( ( C
% 4.36/2.18 = ( G2 @ X2 ) )
% 4.36/2.18 => ( ( member_variable @ X2 @ A )
% 4.36/2.18 => ( member165817296on_trm @ ( produc709594775on_trm @ B3 @ C ) @ ( bNF_Gr400922303on_trm @ A @ F @ G2 ) ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_329_image2__eqI,axiom,
% 4.36/2.18 ! [B3: option_trm,F: char > option_trm,X2: char,C: option_trm,G2: char > option_trm,A: set_char] :
% 4.36/2.18 ( ( B3
% 4.36/2.18 = ( F @ X2 ) )
% 4.36/2.18 => ( ( C
% 4.36/2.18 = ( G2 @ X2 ) )
% 4.36/2.18 => ( ( member_char @ X2 @ A )
% 4.36/2.18 => ( member165817296on_trm @ ( produc709594775on_trm @ B3 @ C ) @ ( bNF_Gr1666135339on_trm @ A @ F @ G2 ) ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_330_image2__eqI,axiom,
% 4.36/2.18 ! [B3: option_fml,F: variable > option_fml,X2: variable,C: option_fml,G2: variable > option_fml,A: set_variable] :
% 4.36/2.18 ( ( B3
% 4.36/2.18 = ( F @ X2 ) )
% 4.36/2.18 => ( ( C
% 4.36/2.18 = ( G2 @ X2 ) )
% 4.36/2.18 => ( ( member_variable @ X2 @ A )
% 4.36/2.18 => ( member1287158352on_fml @ ( produc909629463on_fml @ B3 @ C ) @ ( bNF_Gr600956991on_fml @ A @ F @ G2 ) ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_331_image2__eqI,axiom,
% 4.36/2.18 ! [B3: option_fml,F: char > option_fml,X2: char,C: option_fml,G2: char > option_fml,A: set_char] :
% 4.36/2.18 ( ( B3
% 4.36/2.18 = ( F @ X2 ) )
% 4.36/2.18 => ( ( C
% 4.36/2.18 = ( G2 @ X2 ) )
% 4.36/2.18 => ( ( member_char @ X2 @ A )
% 4.36/2.18 => ( member1287158352on_fml @ ( produc909629463on_fml @ B3 @ C ) @ ( bNF_Gr1866170027on_fml @ A @ F @ G2 ) ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_332_image2__eqI,axiom,
% 4.36/2.18 ! [B3: char,F: variable > char,X2: variable,C: option_trm,G2: variable > option_trm,A: set_variable] :
% 4.36/2.18 ( ( B3
% 4.36/2.18 = ( F @ X2 ) )
% 4.36/2.18 => ( ( C
% 4.36/2.18 = ( G2 @ X2 ) )
% 4.36/2.18 => ( ( member_variable @ X2 @ A )
% 4.36/2.18 => ( member694524327on_trm @ ( produc1500300866on_trm @ B3 @ C ) @ ( bNF_Gr1933470746on_trm @ A @ F @ G2 ) ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_333_image2__eqI,axiom,
% 4.36/2.18 ! [B3: char,F: char > char,X2: char,C: option_trm,G2: char > option_trm,A: set_char] :
% 4.36/2.18 ( ( B3
% 4.36/2.18 = ( F @ X2 ) )
% 4.36/2.18 => ( ( C
% 4.36/2.18 = ( G2 @ X2 ) )
% 4.36/2.18 => ( ( member_char @ X2 @ A )
% 4.36/2.18 => ( member694524327on_trm @ ( produc1500300866on_trm @ B3 @ C ) @ ( bNF_Gr951178926on_trm @ A @ F @ G2 ) ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_334_image2__eqI,axiom,
% 4.36/2.18 ! [B3: set_variable,F: variable > set_variable,X2: variable,C: trm,G2: variable > trm,A: set_variable] :
% 4.36/2.18 ( ( B3
% 4.36/2.18 = ( F @ X2 ) )
% 4.36/2.18 => ( ( C
% 4.36/2.18 = ( G2 @ X2 ) )
% 4.36/2.18 => ( ( member_variable @ X2 @ A )
% 4.36/2.18 => ( member2122665623le_trm @ ( produc1482344242le_trm @ B3 @ C ) @ ( bNF_Gr1330108682le_trm @ A @ F @ G2 ) ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_335_image2__eqI,axiom,
% 4.36/2.18 ! [B3: set_variable,F: char > set_variable,X2: char,C: trm,G2: char > trm,A: set_char] :
% 4.36/2.18 ( ( B3
% 4.36/2.18 = ( F @ X2 ) )
% 4.36/2.18 => ( ( C
% 4.36/2.18 = ( G2 @ X2 ) )
% 4.36/2.18 => ( ( member_char @ X2 @ A )
% 4.36/2.18 => ( member2122665623le_trm @ ( produc1482344242le_trm @ B3 @ C ) @ ( bNF_Gr852774302le_trm @ A @ F @ G2 ) ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_336_Testo_Osimps_I1_J,axiom,
% 4.36/2.18 ! [Phi: fml] :
% 4.36/2.18 ( ( uSubst1367128042_Testo @ ( some_fml @ Phi ) )
% 4.36/2.18 = ( some_game @ ( test @ Phi ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_337_Testo_Opelims,axiom,
% 4.36/2.18 ! [X2: option_fml,Y2: option_game] :
% 4.36/2.18 ( ( ( uSubst1367128042_Testo @ X2 )
% 4.36/2.18 = Y2 )
% 4.36/2.18 => ( ( accp_option_fml @ uSubst954181007to_rel @ X2 )
% 4.36/2.18 => ( ! [Phi2: fml] :
% 4.36/2.18 ( ( X2
% 4.36/2.18 = ( some_fml @ Phi2 ) )
% 4.36/2.18 => ( ( Y2
% 4.36/2.18 = ( some_game @ ( test @ Phi2 ) ) )
% 4.36/2.18 => ~ ( accp_option_fml @ uSubst954181007to_rel @ ( some_fml @ Phi2 ) ) ) )
% 4.36/2.18 => ~ ( ( X2 = none_fml )
% 4.36/2.18 => ( ( Y2 = none_game )
% 4.36/2.18 => ~ ( accp_option_fml @ uSubst954181007to_rel @ none_fml ) ) ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_338_relImage__def,axiom,
% 4.36/2.18 ( bNF_Gr806120164on_fml
% 4.36/2.18 = ( ^ [R6: set_Pr927595527on_fml,F2: option_fml > option_fml] :
% 4.36/2.18 ( collec670974098on_fml
% 4.36/2.18 @ ^ [Uu: produc46605351on_fml] :
% 4.36/2.18 ? [A12: option_fml,A22: option_fml] :
% 4.36/2.18 ( ( Uu
% 4.36/2.18 = ( produc909629463on_fml @ ( F2 @ A12 ) @ ( F2 @ A22 ) ) )
% 4.36/2.18 & ( member1287158352on_fml @ ( produc909629463on_fml @ A12 @ A22 ) @ R6 ) ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_339_Assigno__undef,axiom,
% 4.36/2.18 ! [X2: variable,Theta: option_trm] :
% 4.36/2.18 ( ( ( uSubst834381837ssigno @ X2 @ Theta )
% 4.36/2.18 = none_game )
% 4.36/2.18 = ( Theta = none_trm ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_340_Assigno_Osimps_I2_J,axiom,
% 4.36/2.18 ! [X2: variable] :
% 4.36/2.18 ( ( uSubst834381837ssigno @ X2 @ none_trm )
% 4.36/2.18 = none_game ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_341_Assigno_Oelims,axiom,
% 4.36/2.18 ! [X2: variable,Xa: option_trm,Y2: option_game] :
% 4.36/2.18 ( ( ( uSubst834381837ssigno @ X2 @ Xa )
% 4.36/2.18 = Y2 )
% 4.36/2.18 => ( ! [Theta2: trm] :
% 4.36/2.18 ( ( Xa
% 4.36/2.18 = ( some_trm @ Theta2 ) )
% 4.36/2.18 => ( Y2
% 4.36/2.18 != ( some_game @ ( assign @ X2 @ Theta2 ) ) ) )
% 4.36/2.18 => ~ ( ( Xa = none_trm )
% 4.36/2.18 => ( Y2 != none_game ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_342_Assigno_Opelims,axiom,
% 4.36/2.18 ! [X2: variable,Xa: option_trm,Y2: option_game] :
% 4.36/2.18 ( ( ( uSubst834381837ssigno @ X2 @ Xa )
% 4.36/2.18 = Y2 )
% 4.36/2.18 => ( ( accp_P394694195on_trm @ uSubst157155628no_rel @ ( produc1743721902on_trm @ X2 @ Xa ) )
% 4.36/2.18 => ( ! [Theta2: trm] :
% 4.36/2.18 ( ( Xa
% 4.36/2.18 = ( some_trm @ Theta2 ) )
% 4.36/2.18 => ( ( Y2
% 4.36/2.18 = ( some_game @ ( assign @ X2 @ Theta2 ) ) )
% 4.36/2.18 => ~ ( accp_P394694195on_trm @ uSubst157155628no_rel @ ( produc1743721902on_trm @ X2 @ ( some_trm @ Theta2 ) ) ) ) )
% 4.36/2.18 => ~ ( ( Xa = none_trm )
% 4.36/2.18 => ( ( Y2 = none_game )
% 4.36/2.18 => ~ ( accp_P394694195on_trm @ uSubst157155628no_rel @ ( produc1743721902on_trm @ X2 @ none_trm ) ) ) ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_343_game_Oinject_I2_J,axiom,
% 4.36/2.18 ! [X21: variable,X22: trm,Y21: variable,Y22: trm] :
% 4.36/2.18 ( ( ( assign @ X21 @ X22 )
% 4.36/2.18 = ( assign @ Y21 @ Y22 ) )
% 4.36/2.18 = ( ( X21 = Y21 )
% 4.36/2.18 & ( X22 = Y22 ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_344_game_Odistinct_I15_J,axiom,
% 4.36/2.18 ! [X21: variable,X22: trm,X32: fml] :
% 4.36/2.18 ( ( assign @ X21 @ X22 )
% 4.36/2.18 != ( test @ X32 ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_345_Assigno_Osimps_I1_J,axiom,
% 4.36/2.18 ! [X2: variable,Theta: trm] :
% 4.36/2.18 ( ( uSubst834381837ssigno @ X2 @ ( some_trm @ Theta ) )
% 4.36/2.18 = ( some_game @ ( assign @ X2 @ Theta ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_346_ODEo__undef,axiom,
% 4.36/2.18 ! [X2: char,Theta: option_trm] :
% 4.36/2.18 ( ( ( uSubst1827052306e_ODEo @ X2 @ Theta )
% 4.36/2.18 = none_game )
% 4.36/2.18 = ( Theta = none_trm ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_347_ODEo_Osimps_I2_J,axiom,
% 4.36/2.18 ! [X2: char] :
% 4.36/2.18 ( ( uSubst1827052306e_ODEo @ X2 @ none_trm )
% 4.36/2.18 = none_game ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_348_ODEo_Oelims,axiom,
% 4.36/2.18 ! [X2: char,Xa: option_trm,Y2: option_game] :
% 4.36/2.18 ( ( ( uSubst1827052306e_ODEo @ X2 @ Xa )
% 4.36/2.18 = Y2 )
% 4.36/2.18 => ( ! [Theta2: trm] :
% 4.36/2.18 ( ( Xa
% 4.36/2.18 = ( some_trm @ Theta2 ) )
% 4.36/2.18 => ( Y2
% 4.36/2.18 != ( some_game @ ( ode @ X2 @ Theta2 ) ) ) )
% 4.36/2.18 => ~ ( ( Xa = none_trm )
% 4.36/2.18 => ( Y2 != none_game ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_349_ODEo_Opelims,axiom,
% 4.36/2.18 ! [X2: char,Xa: option_trm,Y2: option_game] :
% 4.36/2.18 ( ( ( uSubst1827052306e_ODEo @ X2 @ Xa )
% 4.36/2.18 = Y2 )
% 4.36/2.18 => ( ( accp_P419951815on_trm @ uSubst299938919Eo_rel @ ( produc1500300866on_trm @ X2 @ Xa ) )
% 4.36/2.18 => ( ! [Theta2: trm] :
% 4.36/2.18 ( ( Xa
% 4.36/2.18 = ( some_trm @ Theta2 ) )
% 4.36/2.18 => ( ( Y2
% 4.36/2.18 = ( some_game @ ( ode @ X2 @ Theta2 ) ) )
% 4.36/2.18 => ~ ( accp_P419951815on_trm @ uSubst299938919Eo_rel @ ( produc1500300866on_trm @ X2 @ ( some_trm @ Theta2 ) ) ) ) )
% 4.36/2.18 => ~ ( ( Xa = none_trm )
% 4.36/2.18 => ( ( Y2 = none_game )
% 4.36/2.18 => ~ ( accp_P419951815on_trm @ uSubst299938919Eo_rel @ ( produc1500300866on_trm @ X2 @ none_trm ) ) ) ) ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_350_game_Oinject_I8_J,axiom,
% 4.36/2.18 ! [X81: char,X82: trm,Y81: char,Y82: trm] :
% 4.36/2.18 ( ( ( ode @ X81 @ X82 )
% 4.36/2.18 = ( ode @ Y81 @ Y82 ) )
% 4.36/2.18 = ( ( X81 = Y81 )
% 4.36/2.18 & ( X82 = Y82 ) ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(fact_351_game_Odistinct_I35_J,axiom,
% 4.36/2.18 ! [X32: fml,X81: char,X82: trm] :
% 4.36/2.18 ( ( test @ X32 )
% 4.36/2.18 != ( ode @ X81 @ X82 ) ) ).
% 4.36/2.18
% 4.36/2.18 thf(conj_0,conjecture,
% 4.36/2.18 ( ( uSubst516392818stappt @ sigma @ ua @ theta )
% 4.36/2.18 != none_trm ) ).
% 4.36/2.18 ------------------------
% 4.43/2.23 % (26729)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_26624 for (2999ds/18Mi)
% 4.43/2.23 % (26724)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_26624 for (2999ds/4Mi)
% 4.43/2.23 % (26726)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_26624 for (2999ds/2Mi)
% 4.43/2.23 % (26725)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_26624 for (2999ds/27Mi)
% 4.43/2.23 % (26728)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_26624 for (2999ds/275Mi)
% 4.43/2.23 % (26727)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_26624 for (2999ds/2Mi)
% 4.43/2.23 % (26723)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_26624 for (2999ds/183Mi)
% 4.43/2.24 % (26726)Instruction limit reached!
% 4.43/2.24 % (26726)------------------------------
% 4.43/2.24 % (26726)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.43/2.24 % (26726)Termination reason: Unknown
% 4.43/2.24 % (26727)Instruction limit reached!
% 4.43/2.24 % (26727)------------------------------
% 4.43/2.24 % (26727)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.43/2.24 % (26726)Termination phase: shuffling
% 4.43/2.24
% 4.43/2.24 % (26726)Memory used [KB]: 1535
% 4.43/2.24 % (26726)Time elapsed: 0.004 s
% 4.43/2.24 % (26726)Instructions burned: 3 (million)
% 4.43/2.24 % (26726)------------------------------
% 4.43/2.24 % (26726)------------------------------
% 4.43/2.24 % (26727)Termination reason: Unknown
% 4.43/2.24 % (26727)Termination phase: shuffling
% 4.43/2.24
% 4.43/2.24 % (26727)Memory used [KB]: 1663
% 4.43/2.24 % (26727)Time elapsed: 0.004 s
% 4.43/2.24 % (26727)Instructions burned: 3 (million)
% 4.43/2.24 % (26727)------------------------------
% 4.43/2.24 % (26727)------------------------------
% 4.43/2.24 % (26724)Instruction limit reached!
% 4.43/2.24 % (26724)------------------------------
% 4.43/2.24 % (26724)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.43/2.24 % (26724)Termination reason: Unknown
% 4.43/2.24 % (26724)Termination phase: shuffling
% 4.43/2.24
% 4.43/2.24 % (26724)Memory used [KB]: 1663
% 4.43/2.24 % (26724)Time elapsed: 0.005 s
% 4.43/2.24 % (26724)Instructions burned: 4 (million)
% 4.43/2.24 % (26724)------------------------------
% 4.43/2.24 % (26724)------------------------------
% 4.43/2.24 % (26729)Instruction limit reached!
% 4.43/2.24 % (26729)------------------------------
% 4.43/2.24 % (26729)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.43/2.24 % (26729)Termination reason: Unknown
% 4.43/2.24 % (26729)Termination phase: shuffling
% 4.43/2.24
% 4.43/2.24 % (26729)Memory used [KB]: 2046
% 4.43/2.24 % (26729)Time elapsed: 0.013 s
% 4.43/2.24 % (26729)Instructions burned: 19 (million)
% 4.43/2.24 % (26729)------------------------------
% 4.43/2.24 % (26729)------------------------------
% 4.43/2.25 % (26725)Instruction limit reached!
% 4.43/2.25 % (26725)------------------------------
% 4.43/2.25 % (26725)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.43/2.25 % (26725)Termination reason: Unknown
% 4.43/2.25 % (26725)Termination phase: shuffling
% 4.43/2.25
% 4.43/2.25 % (26725)Memory used [KB]: 2174
% 4.43/2.25 % (26725)Time elapsed: 0.018 s
% 4.43/2.25 % (26725)Instructions burned: 28 (million)
% 4.43/2.25 % (26725)------------------------------
% 4.43/2.25 % (26725)------------------------------
% 4.43/2.26 % (26731)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_26624 for (2999ds/37Mi)
% 4.43/2.26 % (26732)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_26624 for (2999ds/15Mi)
% 4.43/2.26 % (26730)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_26624 for (2999ds/3Mi)
% 4.43/2.26 % (26730)Instruction limit reached!
% 4.43/2.26 % (26730)------------------------------
% 4.43/2.26 % (26730)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.43/2.26 % (26730)Termination reason: Unknown
% 4.43/2.26 % (26730)Termination phase: shuffling
% 4.43/2.26
% 4.43/2.26 % (26730)Memory used [KB]: 1663
% 4.43/2.26 % (26730)Time elapsed: 0.004 s
% 4.43/2.26 % (26730)Instructions burned: 3 (million)
% 4.43/2.26 % (26730)------------------------------
% 4.43/2.26 % (26730)------------------------------
% 4.43/2.27 % (26733)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_26624 for (2999ds/3Mi)
% 4.43/2.27 % (26732)Instruction limit reached!
% 4.43/2.27 % (26732)------------------------------
% 4.43/2.27 % (26732)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.43/2.27 % (26732)Termination reason: Unknown
% 4.43/2.27 % (26732)Termination phase: shuffling
% 4.43/2.27
% 4.43/2.27 % (26732)Memory used [KB]: 2046
% 4.43/2.27 % (26732)Time elapsed: 0.011 s
% 4.43/2.27 % (26732)Instructions burned: 16 (million)
% 4.43/2.27 % (26732)------------------------------
% 4.43/2.27 % (26732)------------------------------
% 4.43/2.27 % (26733)Instruction limit reached!
% 4.43/2.27 % (26733)------------------------------
% 4.43/2.27 % (26733)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.43/2.27 % (26733)Termination reason: Unknown
% 4.43/2.27 % (26733)Termination phase: shuffling
% 4.43/2.27
% 4.43/2.27 % (26733)Memory used [KB]: 1663
% 4.43/2.27 % (26733)Time elapsed: 0.005 s
% 4.43/2.27 % (26733)Instructions burned: 4 (million)
% 4.43/2.27 % (26733)------------------------------
% 4.43/2.27 % (26733)------------------------------
% 4.43/2.27 % (26734)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_26624 for (2999ds/1041Mi)
% 4.43/2.28 % (26731)Instruction limit reached!
% 4.43/2.28 % (26731)------------------------------
% 4.43/2.28 % (26731)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.43/2.28 % (26731)Termination reason: Unknown
% 4.43/2.28 % (26731)Termination phase: shuffling
% 4.43/2.28
% 4.43/2.28 % (26731)Memory used [KB]: 2430
% 4.43/2.28 % (26731)Time elapsed: 0.022 s
% 4.43/2.28 % (26731)Instructions burned: 38 (million)
% 4.43/2.28 % (26731)------------------------------
% 4.43/2.28 % (26731)------------------------------
% 4.43/2.28 % (26735)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_26624 for (2999ds/7Mi)
% 4.43/2.28 % (26735)Instruction limit reached!
% 4.43/2.28 % (26735)------------------------------
% 4.43/2.28 % (26735)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.43/2.28 % (26735)Termination reason: Unknown
% 4.43/2.28 % (26735)Termination phase: shuffling
% 4.43/2.28
% 4.43/2.28 % (26735)Memory used [KB]: 1791
% 4.43/2.28 % (26735)Time elapsed: 0.007 s
% 4.43/2.28 % (26735)Instructions burned: 8 (million)
% 4.43/2.28 % (26735)------------------------------
% 4.43/2.28 % (26735)------------------------------
% 4.43/2.29 % (26736)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_26624 for (2999ds/16Mi)
% 4.43/2.29 % (26737)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_26624 for (2999ds/3Mi)
% 4.43/2.29 % (26737)Instruction limit reached!
% 4.43/2.29 % (26737)------------------------------
% 4.43/2.29 % (26737)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.43/2.29 % (26737)Termination reason: Unknown
% 4.43/2.29 % (26737)Termination phase: shuffling
% 4.43/2.29
% 4.43/2.29 % (26737)Memory used [KB]: 1663
% 4.43/2.29 % (26737)Time elapsed: 0.003 s
% 4.43/2.29 % (26737)Instructions burned: 3 (million)
% 4.43/2.29 % (26737)------------------------------
% 4.43/2.29 % (26737)------------------------------
% 4.43/2.30 % (26736)Instruction limit reached!
% 4.43/2.30 % (26736)------------------------------
% 4.43/2.30 % (26736)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.43/2.30 % (26736)Termination reason: Unknown
% 4.43/2.30 % (26736)Termination phase: shuffling
% 4.43/2.30
% 4.43/2.30 % (26736)Memory used [KB]: 2046
% 4.43/2.30 % (26736)Time elapsed: 0.012 s
% 4.43/2.30 % (26736)Instructions burned: 17 (million)
% 4.43/2.30 % (26736)------------------------------
% 4.43/2.30 % (26736)------------------------------
% 4.43/2.30 % (26738)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_26624 for (2999ds/3Mi)
% 4.43/2.30 % (26738)Instruction limit reached!
% 4.43/2.30 % (26738)------------------------------
% 4.43/2.30 % (26738)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.43/2.30 % (26738)Termination reason: Unknown
% 4.43/2.30 % (26738)Termination phase: shuffling
% 4.43/2.30
% 4.43/2.30 % (26738)Memory used [KB]: 1663
% 4.43/2.30 % (26738)Time elapsed: 0.004 s
% 4.43/2.30 % (26738)Instructions burned: 3 (million)
% 4.43/2.30 % (26738)------------------------------
% 4.43/2.30 % (26738)------------------------------
% 4.43/2.30 % (26739)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_26624 for (2999ds/7Mi)
% 4.43/2.31 % (26739)Instruction limit reached!
% 4.43/2.31 % (26739)------------------------------
% 4.43/2.31 % (26739)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.43/2.31 % (26739)Termination reason: Unknown
% 4.43/2.31 % (26739)Termination phase: shuffling
% 4.43/2.31
% 4.43/2.31 % (26739)Memory used [KB]: 1791
% 4.43/2.31 % (26739)Time elapsed: 0.007 s
% 4.43/2.31 % (26739)Instructions burned: 8 (million)
% 4.43/2.31 % (26739)------------------------------
% 4.43/2.31 % (26739)------------------------------
% 4.43/2.31 % (26740)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_26624 for (2999ds/3Mi)
% 4.43/2.31 % (26740)Instruction limit reached!
% 4.43/2.31 % (26740)------------------------------
% 4.43/2.31 % (26740)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.43/2.31 % (26740)Termination reason: Unknown
% 4.43/2.31 % (26740)Termination phase: shuffling
% 4.43/2.31
% 4.43/2.31 % (26740)Memory used [KB]: 1663
% 4.43/2.31 % (26740)Time elapsed: 0.004 s
% 4.43/2.31 % (26740)Instructions burned: 3 (million)
% 4.43/2.31 % (26740)------------------------------
% 4.43/2.31 % (26740)------------------------------
% 4.43/2.31 % (26741)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_26624 for (2998ds/4Mi)
% 4.43/2.32 % (26741)Instruction limit reached!
% 4.43/2.32 % (26741)------------------------------
% 4.43/2.32 % (26741)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.43/2.32 % (26741)Termination reason: Unknown
% 4.43/2.32 % (26741)Termination phase: shuffling
% 4.43/2.32
% 4.43/2.32 % (26741)Memory used [KB]: 1663
% 4.43/2.32 % (26741)Time elapsed: 0.005 s
% 4.43/2.32 % (26741)Instructions burned: 5 (million)
% 4.43/2.32 % (26741)------------------------------
% 4.43/2.32 % (26741)------------------------------
% 4.43/2.32 % (26742)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_26624 for (2998ds/18Mi)
% 4.43/2.33 % (26743)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_26624 for (2998ds/710Mi)
% 4.43/2.33 % (26742)Instruction limit reached!
% 4.43/2.33 % (26742)------------------------------
% 4.43/2.33 % (26742)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.43/2.33 % (26742)Termination reason: Unknown
% 4.43/2.33 % (26742)Termination phase: shuffling
% 4.43/2.33
% 4.43/2.33 % (26742)Memory used [KB]: 2046
% 4.43/2.33 % (26742)Time elapsed: 0.013 s
% 4.43/2.33 % (26742)Instructions burned: 19 (million)
% 4.43/2.33 % (26742)------------------------------
% 4.43/2.33 % (26742)------------------------------
% 4.43/2.33 % (26744)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_26624 for (2998ds/6Mi)
% 4.43/2.33 % (26744)Instruction limit reached!
% 4.43/2.33 % (26744)------------------------------
% 4.43/2.33 % (26744)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.43/2.33 % (26744)Termination reason: Unknown
% 4.43/2.33 % (26744)Termination phase: shuffling
% 4.43/2.33
% 4.43/2.33 % (26744)Memory used [KB]: 1791
% 4.43/2.33 % (26744)Time elapsed: 0.005 s
% 4.43/2.33 % (26744)Instructions burned: 6 (million)
% 4.43/2.33 % (26744)------------------------------
% 4.43/2.33 % (26744)------------------------------
% 4.43/2.33 % (26723)Instruction limit reached!
% 4.43/2.33 % (26723)------------------------------
% 4.43/2.33 % (26723)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.43/2.33 % (26723)Termination reason: Unknown
% 4.43/2.33 % (26723)Termination phase: Saturation
% 4.43/2.33
% 4.43/2.33 % (26723)Memory used [KB]: 7931
% 4.43/2.33 % (26723)Time elapsed: 0.103 s
% 4.43/2.33 % (26723)Instructions burned: 184 (million)
% 4.43/2.33 % (26723)------------------------------
% 4.43/2.33 % (26723)------------------------------
% 4.43/2.34 % (26745)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_26624 for (2998ds/902Mi)
% 4.43/2.35 % (26746)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_26624 for (2998ds/21Mi)
% 4.43/2.35 % (26748)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_26624 for (2998ds/6Mi)
% 4.43/2.35 % (26747)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_26624 for (2998ds/5Mi)
% 4.43/2.36 % (26747)Instruction limit reached!
% 4.43/2.36 % (26747)------------------------------
% 4.43/2.36 % (26747)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.43/2.36 % (26747)Termination reason: Unknown
% 4.43/2.36 % (26747)Termination phase: shuffling
% 4.43/2.36
% 4.43/2.36 % (26747)Memory used [KB]: 1663
% 4.43/2.36 % (26747)Time elapsed: 0.005 s
% 4.43/2.36 % (26747)Instructions burned: 5 (million)
% 4.43/2.36 % (26747)------------------------------
% 4.43/2.36 % (26747)------------------------------
% 4.43/2.36 % (26748)Instruction limit reached!
% 4.43/2.36 % (26748)------------------------------
% 4.43/2.36 % (26748)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.43/2.36 % (26748)Termination reason: Unknown
% 4.43/2.36 % (26748)Termination phase: shuffling
% 4.43/2.36
% 4.43/2.36 % (26748)Memory used [KB]: 1791
% 4.43/2.36 % (26748)Time elapsed: 0.006 s
% 4.43/2.36 % (26748)Instructions burned: 7 (million)
% 4.43/2.36 % (26748)------------------------------
% 4.43/2.36 % (26748)------------------------------
% 4.43/2.36 % (26746)Instruction limit reached!
% 4.43/2.36 % (26746)------------------------------
% 4.43/2.36 % (26746)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.43/2.36 % (26746)Termination reason: Unknown
% 4.43/2.36 % (26746)Termination phase: shuffling
% 4.43/2.36
% 4.43/2.36 % (26746)Memory used [KB]: 2174
% 4.43/2.36 % (26746)Time elapsed: 0.015 s
% 4.43/2.36 % (26746)Instructions burned: 21 (million)
% 4.43/2.36 % (26746)------------------------------
% 4.43/2.36 % (26746)------------------------------
% 4.43/2.38 % (26728)Instruction limit reached!
% 4.43/2.38 % (26728)------------------------------
% 4.43/2.38 % (26728)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.43/2.38 % (26728)Termination reason: Unknown
% 4.43/2.38 % (26728)Termination phase: Saturation
% 4.43/2.38
% 4.43/2.38 % (26728)Memory used [KB]: 7036
% 4.43/2.38 % (26728)Time elapsed: 0.144 s
% 4.43/2.38 % (26728)Instructions burned: 276 (million)
% 4.43/2.38 % (26728)------------------------------
% 4.43/2.38 % (26728)------------------------------
% 4.43/2.38 % (26749)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_26624 for (2998ds/377Mi)
% 4.43/2.38 % (26750)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_26624 for (2998ds/779Mi)
% 4.43/2.38 % (26751)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_26624 for (2998ds/19Mi)
% 4.43/2.39 % (26751)Instruction limit reached!
% 4.43/2.39 % (26751)------------------------------
% 4.43/2.39 % (26751)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.43/2.39 % (26751)Termination reason: Unknown
% 4.43/2.39 % (26751)Termination phase: shuffling
% 4.43/2.39
% 4.43/2.39 % (26751)Memory used [KB]: 2046
% 4.43/2.39 % (26751)Time elapsed: 0.012 s
% 4.43/2.39 % (26751)Instructions burned: 19 (million)
% 4.43/2.39 % (26751)------------------------------
% 4.43/2.39 % (26751)------------------------------
% 4.43/2.40 % (26752)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_26624 for (2998ds/879Mi)
% 4.43/2.41 % (26753)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_26624 for (2997ds/17Mi)
% 4.43/2.42 % (26753)Instruction limit reached!
% 4.43/2.42 % (26753)------------------------------
% 4.43/2.42 % (26753)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.43/2.42 % (26753)Termination reason: Unknown
% 4.43/2.42 % (26753)Termination phase: shuffling
% 4.43/2.42
% 4.43/2.42 % (26753)Memory used [KB]: 1918
% 4.43/2.42 % (26753)Time elapsed: 0.012 s
% 4.43/2.42 % (26753)Instructions burned: 18 (million)
% 4.43/2.42 % (26753)------------------------------
% 4.43/2.42 % (26753)------------------------------
% 4.43/2.44 % (26752)First to succeed.
% 4.43/2.45 % (26754)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_26624 for (2997ds/3Mi)
% 4.43/2.45 % (26752)Refutation found. Thanks to Tanya!
% 4.43/2.45 % SZS status Theorem for DTF2THF_26624
% 4.43/2.45 % SZS output start Proof for DTF2THF_26624
% 4.43/2.45 thf(type_def_5, type, set_char: $tType).
% 4.43/2.45 thf(type_def_6, type, char: $tType).
% 4.43/2.45 thf(type_def_7, type, option_fml: $tType).
% 4.43/2.45 thf(type_def_9, type, set_Pr927595527on_fml: $tType).
% 4.43/2.45 thf(type_def_10, type, option_game: $tType).
% 4.43/2.45 thf(type_def_11, type, set_Pr622314946on_fml: $tType).
% 4.43/2.45 thf(type_def_12, type, option_trm: $tType).
% 4.43/2.45 thf(type_def_13, type, set_Pr1471344007on_trm: $tType).
% 4.43/2.45 thf(type_def_14, type, set_variable: $tType).
% 4.43/2.45 thf(type_def_15, type, trm: $tType).
% 4.43/2.45 thf(type_def_16, type, set_Pr1235432374le_trm: $tType).
% 4.43/2.45 thf(type_def_17, type, set_Pr943832262on_trm: $tType).
% 4.43/2.45 thf(type_def_18, type, variable: $tType).
% 4.43/2.45 thf(type_def_19, type, real: $tType).
% 4.43/2.45 thf(type_def_20, type, fml: $tType).
% 4.43/2.45 thf(type_def_21, type, game: $tType).
% 4.43/2.45 thf(type_def_22, type, produc1072747943on_trm: $tType).
% 4.43/2.45 thf(type_def_23, type, produc464795408on_trm: $tType).
% 4.43/2.45 thf(type_def_24, type, produc1024976764on_trm: $tType).
% 4.43/2.45 thf(type_def_25, type, denotational_interp: $tType).
% 4.43/2.45 thf(type_def_26, type, produc833882726rp_trm: $tType).
% 4.43/2.45 thf(type_def_27, type, produc46605351on_fml: $tType).
% 4.43/2.45 thf(type_def_28, type, produc1810527345on_trm: $tType).
% 4.43/2.45 thf(type_def_29, type, produc1739631244on_fml: $tType).
% 4.43/2.45 thf(type_def_30, type, produc1016592119n_game: $tType).
% 4.43/2.45 thf(type_def_31, type, produc1456309597on_fml: $tType).
% 4.43/2.45 thf(type_def_32, type, produc1418842292n_game: $tType).
% 4.43/2.45 thf(type_def_33, type, produc1367888000le_trm: $tType).
% 4.43/2.45 thf(type_def_34, type, produc1699626005le_trm: $tType).
% 4.43/2.45 thf(type_def_35, type, produc1872652007on_fml: $tType).
% 4.43/2.45 thf(type_def_36, type, produc1158546023on_trm: $tType).
% 4.43/2.45 thf(type_def_37, type, produc1928189433on_fml: $tType).
% 4.43/2.45 thf(type_def_38, type, produc591588199on_fml: $tType).
% 4.43/2.45 thf(type_def_39, type, produc2024965863on_trm: $tType).
% 4.43/2.45 thf(type_def_40, type, produc1279577057le_trm: $tType).
% 4.43/2.45 thf(type_def_41, type, produc2018724225on_trm: $tType).
% 4.43/2.45 thf(type_def_42, type, produc432717079riable: $tType).
% 4.43/2.45 thf(type_def_43, type, produc1593312387r_char: $tType).
% 4.43/2.45 thf(type_def_44, type, product_prod_trm_trm: $tType).
% 4.43/2.45 thf(type_def_45, type, produc1408538418on_fml: $tType).
% 4.43/2.45 thf(type_def_46, type, set_Pr1045337287on_fml: $tType).
% 4.43/2.45 thf(type_def_47, type, set_Pr1588097095on_trm: $tType).
% 4.43/2.45 thf(type_def_48, type, set_Pr1625152599n_game: $tType).
% 4.43/2.45 thf(type_def_49, type, set_Pr1918373977on_fml: $tType).
% 4.43/2.45 thf(type_def_50, type, set_Pr519625031on_fml: $tType).
% 4.43/2.45 thf(type_def_51, type, set_Pr1062384839on_trm: $tType).
% 4.43/2.45 thf(type_def_52, type, set_Pr181266295riable: $tType).
% 4.43/2.45 thf(type_def_53, type, set_Pr491793543rm_trm: $tType).
% 4.43/2.45 thf(type_def_54, type, set_Pr1969262145le_trm: $tType).
% 4.43/2.45 thf(type_def_55, type, set_Pr604539619r_char: $tType).
% 4.43/2.45 thf(type_def_56, type, set_Pr1481565921on_trm: $tType).
% 4.43/2.45 thf(func_def_0, type, produc1699626005le_trm: $tType).
% 4.43/2.45 thf(func_def_1, type, produc1418842292n_game: $tType).
% 4.43/2.45 thf(func_def_2, type, set_Pr1918373977on_fml: $tType).
% 4.43/2.45 thf(func_def_3, type, set_Pr1062384839on_trm: $tType).
% 4.43/2.45 thf(func_def_4, type, set_Pr519625031on_fml: $tType).
% 4.43/2.45 thf(func_def_5, type, set_Pr1588097095on_trm: $tType).
% 4.43/2.45 thf(func_def_6, type, set_Pr1045337287on_fml: $tType).
% 4.43/2.45 thf(func_def_7, type, produc1928189433on_fml: $tType).
% 4.43/2.45 thf(func_def_8, type, produc2024965863on_trm: $tType).
% 4.43/2.45 thf(func_def_9, type, produc591588199on_fml: $tType).
% 4.43/2.45 thf(func_def_10, type, produc1158546023on_trm: $tType).
% 4.43/2.45 thf(func_def_11, type, produc1872652007on_fml: $tType).
% 4.43/2.45 thf(func_def_12, type, set_Pr1481565921on_trm: $tType).
% 4.43/2.45 thf(func_def_13, type, set_Pr1969262145le_trm: $tType).
% 4.43/2.45 thf(func_def_14, type, produc2018724225on_trm: $tType).
% 4.43/2.45 thf(func_def_15, type, produc1279577057le_trm: $tType).
% 4.43/2.45 thf(func_def_16, type, set_Pr1625152599n_game: $tType).
% 4.43/2.45 thf(func_def_17, type, set_Pr622314946on_fml: $tType).
% 4.43/2.45 thf(func_def_18, type, set_Pr1471344007on_trm: $tType).
% 4.43/2.45 thf(func_def_19, type, set_Pr927595527on_fml: $tType).
% 4.43/2.45 thf(func_def_20, type, set_Pr181266295riable: $tType).
% 4.43/2.45 thf(func_def_21, type, produc1016592119n_game: $tType).
% 4.43/2.45 thf(func_def_22, type, produc1739631244on_fml: $tType).
% 4.43/2.45 thf(func_def_23, type, produc1072747943on_trm: $tType).
% 4.43/2.45 thf(func_def_24, type, produc1456309597on_fml: $tType).
% 4.43/2.45 thf(func_def_25, type, produc1810527345on_trm: $tType).
% 4.43/2.45 thf(func_def_26, type, produc46605351on_fml: $tType).
% 4.43/2.45 thf(func_def_27, type, produc432717079riable: $tType).
% 4.43/2.45 thf(func_def_28, type, set_Pr943832262on_trm: $tType).
% 4.43/2.45 thf(func_def_29, type, set_Pr1235432374le_trm: $tType).
% 4.43/2.45 thf(func_def_30, type, produc1024976764on_trm: $tType).
% 4.43/2.45 thf(func_def_31, type, produc1408538418on_fml: $tType).
% 4.43/2.45 thf(func_def_32, type, produc464795408on_trm: $tType).
% 4.43/2.45 thf(func_def_33, type, produc833882726rp_trm: $tType).
% 4.43/2.45 thf(func_def_34, type, produc1367888000le_trm: $tType).
% 4.43/2.45 thf(func_def_35, type, set_Pr604539619r_char: $tType).
% 4.43/2.45 thf(func_def_36, type, set_Pr491793543rm_trm: $tType).
% 4.43/2.45 thf(func_def_37, type, produc1593312387r_char: $tType).
% 4.43/2.45 thf(func_def_38, type, product_prod_trm_trm: $tType).
% 4.43/2.45 thf(func_def_39, type, option_game: $tType).
% 4.43/2.45 thf(func_def_40, type, option_trm: $tType).
% 4.43/2.45 thf(func_def_41, type, option_fml: $tType).
% 4.43/2.45 thf(func_def_42, type, denotational_interp: $tType).
% 4.43/2.45 thf(func_def_43, type, set_variable: $tType).
% 4.43/2.45 thf(func_def_44, type, set_char: $tType).
% 4.43/2.45 thf(func_def_45, type, variable: $tType).
% 4.43/2.45 thf(func_def_46, type, game: $tType).
% 4.43/2.45 thf(func_def_47, type, char: $tType).
% 4.43/2.45 thf(func_def_48, type, trm: $tType).
% 4.43/2.45 thf(func_def_49, type, fml: $tType).
% 4.43/2.45 thf(func_def_50, type, real: $tType).
% 4.43/2.45 thf(func_def_51, type, bNF_Gr1866170027on_fml: set_char > (char > option_fml) > (char > option_fml) > set_Pr927595527on_fml).
% 4.43/2.45 thf(func_def_52, type, bNF_Gr756940202on_fml: set_char > (char > option_game) > (char > option_fml) > set_Pr622314946on_fml).
% 4.43/2.45 thf(func_def_53, type, bNF_Gr1666135339on_trm: set_char > (char > option_trm) > (char > option_trm) > set_Pr1471344007on_trm).
% 4.43/2.45 thf(func_def_54, type, bNF_Gr852774302le_trm: set_char > (char > set_variable) > (char > trm) > set_Pr1235432374le_trm).
% 4.43/2.45 thf(func_def_55, type, bNF_Gr951178926on_trm: set_char > (char > char) > (char > option_trm) > set_Pr943832262on_trm).
% 4.43/2.45 thf(func_def_56, type, bNF_Gr600956991on_fml: set_variable > (variable > option_fml) > (variable > option_fml) > set_Pr927595527on_fml).
% 4.43/2.45 thf(func_def_57, type, bNF_Gr2142503190on_fml: set_variable > (variable > option_game) > (variable > option_fml) > set_Pr622314946on_fml).
% 4.43/2.45 thf(func_def_58, type, bNF_Gr400922303on_trm: set_variable > (variable > option_trm) > (variable > option_trm) > set_Pr1471344007on_trm).
% 4.43/2.45 thf(func_def_59, type, bNF_Gr1330108682le_trm: set_variable > (variable > set_variable) > (variable > trm) > set_Pr1235432374le_trm).
% 4.43/2.45 thf(func_def_60, type, bNF_Gr1933470746on_trm: set_variable > (variable > char) > (variable > option_trm) > set_Pr943832262on_trm).
% 4.43/2.45 thf(func_def_61, type, bNF_Gr806120164on_fml: set_Pr927595527on_fml > (option_fml > option_fml) > set_Pr927595527on_fml).
% 4.43/2.45 thf(func_def_62, type, denota1419872369iation: (variable > real) > (variable > real) > set_variable > $o).
% 4.43/2.45 thf(func_def_63, type, none_fml: option_fml).
% 4.43/2.45 thf(func_def_64, type, none_game: option_game).
% 4.43/2.45 thf(func_def_65, type, none_trm: option_trm).
% 4.43/2.45 thf(func_def_66, type, some_fml: fml > option_fml).
% 4.43/2.45 thf(func_def_67, type, some_game: game > option_game).
% 4.43/2.45 thf(func_def_68, type, some_trm: trm > option_trm).
% 4.43/2.45 thf(func_def_69, type, case_option_o_fml: $o > (fml > $o) > option_fml > $o).
% 4.43/2.45 thf(func_def_70, type, case_option_o_game: $o > (game > $o) > option_game > $o).
% 4.43/2.45 thf(func_def_71, type, case_option_o_trm: $o > (trm > $o) > option_trm > $o).
% 4.43/2.45 thf(func_def_72, type, the_fml: option_fml > fml).
% 4.43/2.45 thf(func_def_73, type, the_game: option_game > game).
% 4.43/2.45 thf(func_def_74, type, the_trm: option_trm > trm).
% 4.43/2.45 thf(func_def_75, type, ord_le802833166_fml_o: (option_fml > option_fml > $o) > (option_fml > option_fml > $o) > $o).
% 4.43/2.45 thf(func_def_76, type, ord_le181580155_fml_o: (option_fml > $o) > (option_fml > $o) > $o).
% 4.43/2.45 thf(func_def_77, type, ord_le1588489637_fml_o: (option_game > option_fml > $o) > (option_game > option_fml > $o) > $o).
% 4.43/2.45 thf(func_def_78, type, ord_le847028878_trm_o: (option_trm > option_trm > $o) > (option_trm > option_trm > $o) > $o).
% 4.43/2.45 thf(func_def_79, type, ord_le1957133745_trm_o: (option_trm > $o) > (option_trm > $o) > $o).
% 4.43/2.45 thf(func_def_80, type, ord_le90123726_trm_o: (produc1072747943on_trm > produc1072747943on_trm > $o) > (produc1072747943on_trm > produc1072747943on_trm > $o) > $o).
% 4.43/2.45 thf(func_def_81, type, ord_le1721128566_trm_o: (produc1072747943on_trm > $o) > (produc1072747943on_trm > $o) > $o).
% 4.43/2.45 thf(func_def_82, type, ord_le157637894_trm_o: (produc464795408on_trm > produc464795408on_trm > $o) > (produc464795408on_trm > produc464795408on_trm > $o) > $o).
% 4.43/2.45 thf(func_def_83, type, ord_le1222882015_trm_o: (produc464795408on_trm > $o) > (produc464795408on_trm > $o) > $o).
% 4.43/2.45 thf(func_def_84, type, ord_le370603054_trm_o: (produc1024976764on_trm > produc1024976764on_trm > $o) > (produc1024976764on_trm > produc1024976764on_trm > $o) > $o).
% 4.43/2.45 thf(func_def_85, type, ord_le373274227_trm_o: (produc1024976764on_trm > $o) > (produc1024976764on_trm > $o) > $o).
% 4.43/2.45 thf(func_def_86, type, ord_le691957041_trm_o: (set_variable > trm > $o) > (set_variable > trm > $o) > $o).
% 4.43/2.45 thf(func_def_87, type, ord_le1890124833_trm_o: (char > option_trm > $o) > (char > option_trm > $o) > $o).
% 4.43/2.45 thf(func_def_88, type, ord_less_eq_char_o: (char > $o) > (char > $o) > $o).
% 4.43/2.45 thf(func_def_89, type, ord_le1407353162able_o: (variable > $o) > (variable > $o) > $o).
% 4.43/2.45 thf(func_def_90, type, ord_le778974119on_fml: set_Pr927595527on_fml > set_Pr927595527on_fml > $o).
% 4.43/2.45 thf(func_def_91, type, ord_le782333474on_fml: set_Pr622314946on_fml > set_Pr622314946on_fml > $o).
% 4.43/2.45 thf(func_def_92, type, ord_le1322722599on_trm: set_Pr1471344007on_trm > set_Pr1471344007on_trm > $o).
% 4.43/2.45 thf(func_def_93, type, ord_le2102862870le_trm: set_Pr1235432374le_trm > set_Pr1235432374le_trm > $o).
% 4.43/2.45 thf(func_def_94, type, ord_le541293862on_trm: set_Pr943832262on_trm > set_Pr943832262on_trm > $o).
% 4.43/2.45 thf(func_def_95, type, ord_less_eq_set_char: set_char > set_char > $o).
% 4.43/2.45 thf(func_def_96, type, ord_le282106107riable: set_variable > set_variable > $o).
% 4.43/2.45 thf(func_def_97, type, order_272405634riable: (set_variable > $o) > set_variable).
% 4.43/2.45 thf(func_def_98, type, produc1132922070rp_trm: denotational_interp > trm > produc833882726rp_trm).
% 4.43/2.45 thf(func_def_99, type, produc909629463on_fml: option_fml > option_fml > produc46605351on_fml).
% 4.43/2.45 thf(func_def_100, type, produc1447374177on_trm: option_fml > option_trm > produc1810527345on_trm).
% 4.43/2.45 thf(func_def_101, type, produc2124676926on_fml: option_game > option_fml > produc1739631244on_fml).
% 4.43/2.45 thf(func_def_102, type, produc1111617711n_game: option_game > option_game > produc1016592119n_game).
% 4.43/2.45 thf(func_def_103, type, produc171850061on_fml: option_trm > option_fml > produc1456309597on_fml).
% 4.43/2.45 thf(func_def_104, type, produc709594775on_trm: option_trm > option_trm > produc1072747943on_trm).
% 4.43/2.45 thf(func_def_105, type, produc2015636557le_trm: produc1418842292n_game > produc1367888000le_trm > produc1699626005le_trm).
% 4.43/2.45 thf(func_def_106, type, produc1367044951on_fml: produc46605351on_fml > produc46605351on_fml > produc1872652007on_fml).
% 4.43/2.45 thf(func_def_107, type, produc2132972503on_trm: produc1810527345on_trm > produc1810527345on_trm > produc1158546023on_trm).
% 4.43/2.45 thf(func_def_108, type, produc556056113on_fml: produc1739631244on_fml > produc1739631244on_fml > produc1928189433on_fml).
% 4.43/2.45 thf(func_def_109, type, produc1235825367on_fml: produc1456309597on_fml > produc1456309597on_fml > produc591588199on_fml).
% 4.43/2.45 thf(func_def_110, type, produc2001752919on_trm: produc1072747943on_trm > produc1072747943on_trm > produc2024965863on_trm).
% 4.43/2.45 thf(func_def_111, type, produc1056455193le_trm: produc1367888000le_trm > produc1367888000le_trm > produc1279577057le_trm).
% 4.43/2.45 thf(func_def_112, type, produc444919481on_trm: produc464795408on_trm > produc464795408on_trm > produc2018724225on_trm).
% 4.43/2.45 thf(func_def_113, type, produc1766592463riable: set_variable > set_variable > produc432717079riable).
% 4.43/2.45 thf(func_def_114, type, produc1482344242le_trm: set_variable > trm > produc1367888000le_trm).
% 4.43/2.45 thf(func_def_115, type, produc1500300866on_trm: char > option_trm > produc464795408on_trm).
% 4.43/2.45 thf(func_def_116, type, produc19545147r_char: char > char > produc1593312387r_char).
% 4.43/2.45 thf(func_def_117, type, product_Pair_trm_trm: trm > trm > product_prod_trm_trm).
% 4.43/2.45 thf(func_def_118, type, produc1205977188on_fml: variable > option_fml > produc1408538418on_fml).
% 4.43/2.45 thf(func_def_119, type, produc1743721902on_trm: variable > option_trm > produc1024976764on_trm).
% 4.43/2.45 thf(func_def_120, type, collec670974098on_fml: (produc46605351on_fml > $o) > set_Pr927595527on_fml).
% 4.43/2.45 thf(func_def_121, type, collec749447393on_fml: (produc1739631244on_fml > $o) > set_Pr622314946on_fml).
% 4.43/2.45 thf(func_def_122, type, collec1697116690on_trm: (produc1072747943on_trm > $o) > set_Pr1471344007on_trm).
% 4.43/2.45 thf(func_def_123, type, collec575343829le_trm: (produc1367888000le_trm > $o) > set_Pr1235432374le_trm).
% 4.43/2.45 thf(func_def_124, type, collec1756633317on_trm: (produc464795408on_trm > $o) > set_Pr943832262on_trm).
% 4.43/2.45 thf(func_def_125, type, collect_char: (char > $o) > set_char).
% 4.43/2.45 thf(func_def_126, type, collect_variable: (variable > $o) > set_variable).
% 4.43/2.45 thf(func_def_127, type, geq: trm > trm > fml).
% 4.43/2.45 thf(func_def_128, type, assign: variable > trm > game).
% 4.43/2.45 thf(func_def_129, type, ode: char > trm > game).
% 4.43/2.45 thf(func_def_130, type, test: fml > game).
% 4.43/2.45 thf(func_def_131, type, const: char > trm).
% 4.43/2.45 thf(func_def_132, type, differential: trm > trm).
% 4.43/2.45 thf(func_def_133, type, func: char > trm > trm).
% 4.43/2.45 thf(func_def_134, type, number: real > trm).
% 4.43/2.45 thf(func_def_135, type, plus: trm > trm > trm).
% 4.43/2.45 thf(func_def_136, type, times: trm > trm > trm).
% 4.43/2.45 thf(func_def_137, type, var: variable > trm).
% 4.43/2.45 thf(func_def_138, type, uSubst834381837ssigno: variable > option_trm > option_game).
% 4.43/2.45 thf(func_def_139, type, uSubst157155628no_rel: produc1024976764on_trm > produc1024976764on_trm > $o).
% 4.43/2.45 thf(func_def_140, type, uSubst716837505ntialo: option_trm > option_trm).
% 4.43/2.45 thf(func_def_141, type, uSubst2051024824lo_rel: option_trm > option_trm > $o).
% 4.43/2.45 thf(func_def_142, type, uSubst152838031e_Geqo: option_trm > option_trm > option_fml).
% 4.43/2.45 thf(func_def_143, type, uSubst1304144938qo_rel: produc1072747943on_trm > produc1072747943on_trm > $o).
% 4.43/2.45 thf(func_def_144, type, uSubst1827052306e_ODEo: char > option_trm > option_game).
% 4.43/2.45 thf(func_def_145, type, uSubst299938919Eo_rel: produc464795408on_trm > produc464795408on_trm > $o).
% 4.43/2.45 thf(func_def_146, type, uSubst141955042_Pluso: option_trm > option_trm > option_trm).
% 4.43/2.45 thf(func_def_147, type, uSubst691094423so_rel: produc1072747943on_trm > produc1072747943on_trm > $o).
% 4.43/2.45 thf(func_def_148, type, uSubst1367128042_Testo: option_fml > option_game).
% 4.43/2.45 thf(func_def_149, type, uSubst954181007to_rel: option_fml > option_fml > $o).
% 4.43/2.45 thf(func_def_150, type, uSubst918876924Timeso: option_trm > option_trm > option_trm).
% 4.43/2.45 thf(func_def_151, type, uSubst924844285so_rel: produc1072747943on_trm > produc1072747943on_trm > $o).
% 4.43/2.45 thf(func_def_152, type, uSubst1559070963pconst: produc1418842292n_game > set_variable > char > option_trm).
% 4.43/2.45 thf(func_def_153, type, uSubst516392804stappf: produc1418842292n_game > set_variable > fml > option_fml).
% 4.43/2.45 thf(func_def_154, type, uSubst516392818stappt: produc1418842292n_game > set_variable > trm > option_trm).
% 4.43/2.45 thf(func_def_155, type, uSubst1917534215pt_rel: produc1699626005le_trm > produc1699626005le_trm > $o).
% 4.43/2.45 thf(func_def_156, type, accp_option_fml: (option_fml > option_fml > $o) > option_fml > $o).
% 4.43/2.45 thf(func_def_157, type, accp_option_trm: (option_trm > option_trm > $o) > option_trm > $o).
% 4.43/2.45 thf(func_def_158, type, accp_P758790320on_trm: (produc1072747943on_trm > produc1072747943on_trm > $o) > produc1072747943on_trm > $o).
% 4.43/2.45 thf(func_def_159, type, accp_P1877119646le_trm: (produc1699626005le_trm > produc1699626005le_trm > $o) > produc1699626005le_trm > $o).
% 4.43/2.45 thf(func_def_160, type, accp_P419951815on_trm: (produc464795408on_trm > produc464795408on_trm > $o) > produc464795408on_trm > $o).
% 4.43/2.45 thf(func_def_161, type, accp_P394694195on_trm: (produc1024976764on_trm > produc1024976764on_trm > $o) > produc1024976764on_trm > $o).
% 4.43/2.45 thf(func_def_162, type, lex_pr314879023on_fml: set_Pr927595527on_fml > set_Pr927595527on_fml > set_Pr1045337287on_fml).
% 4.43/2.45 thf(func_def_163, type, lex_pr852623737on_trm: set_Pr927595527on_fml > set_Pr1471344007on_trm > set_Pr1588097095on_trm).
% 4.43/2.45 thf(func_def_164, type, lex_pr425996582on_fml: set_Pr1625152599n_game > set_Pr927595527on_fml > set_Pr1918373977on_fml).
% 4.43/2.45 thf(func_def_165, type, lex_pr1724583269on_fml: set_Pr1471344007on_trm > set_Pr927595527on_fml > set_Pr519625031on_fml).
% 4.43/2.45 thf(func_def_166, type, lex_pr114844335on_trm: set_Pr1471344007on_trm > set_Pr1471344007on_trm > set_Pr1062384839on_trm).
% 4.43/2.45 thf(func_def_167, type, lex_pr1522821402le_trm: set_Pr181266295riable > set_Pr491793543rm_trm > set_Pr1969262145le_trm).
% 4.43/2.45 thf(func_def_168, type, lex_pr1901327402on_trm: set_Pr604539619r_char > set_Pr1471344007on_trm > set_Pr1481565921on_trm).
% 4.43/2.45 thf(func_def_169, type, member1287158352on_fml: produc46605351on_fml > set_Pr927595527on_fml > $o).
% 4.43/2.45 thf(func_def_170, type, member1883102883on_fml: produc1739631244on_fml > set_Pr622314946on_fml > $o).
% 4.43/2.45 thf(func_def_171, type, member191809696n_game: produc1016592119n_game > set_Pr1625152599n_game > $o).
% 4.43/2.45 thf(func_def_172, type, member165817296on_trm: produc1072747943on_trm > set_Pr1471344007on_trm > $o).
% 4.43/2.45 thf(func_def_173, type, member450497296on_fml: produc1872652007on_fml > set_Pr1045337287on_fml > $o).
% 4.43/2.45 thf(func_def_174, type, member1883874960on_trm: produc1158546023on_trm > set_Pr1588097095on_trm > $o).
% 4.43/2.45 thf(func_def_175, type, member113767842on_fml: produc1928189433on_fml > set_Pr1918373977on_fml > $o).
% 4.43/2.45 thf(func_def_176, type, member1316917136on_fml: produc591588199on_fml > set_Pr519625031on_fml > $o).
% 4.43/2.45 thf(func_def_177, type, member602811152on_trm: produc2024965863on_trm > set_Pr1062384839on_trm > $o).
% 4.43/2.45 thf(func_def_178, type, member1150310282le_trm: produc1279577057le_trm > set_Pr1969262145le_trm > $o).
% 4.43/2.45 thf(func_def_179, type, member1950256170on_trm: produc2018724225on_trm > set_Pr1481565921on_trm > $o).
% 4.43/2.45 thf(func_def_180, type, member1978718144riable: produc432717079riable > set_Pr181266295riable > $o).
% 4.43/2.45 thf(func_def_181, type, member2122665623le_trm: produc1367888000le_trm > set_Pr1235432374le_trm > $o).
% 4.43/2.45 thf(func_def_182, type, member694524327on_trm: produc464795408on_trm > set_Pr943832262on_trm > $o).
% 4.43/2.45 thf(func_def_183, type, member1866856748r_char: produc1593312387r_char > set_Pr604539619r_char > $o).
% 4.43/2.45 thf(func_def_184, type, member1735386832rm_trm: product_prod_trm_trm > set_Pr491793543rm_trm > $o).
% 4.43/2.45 thf(func_def_185, type, member_char: char > set_char > $o).
% 4.43/2.45 thf(func_def_186, type, member_variable: variable > set_variable > $o).
% 4.43/2.45 thf(func_def_187, type, u: set_variable).
% 4.43/2.45 thf(func_def_188, type, ua: set_variable).
% 4.43/2.45 thf(func_def_189, type, eta: trm).
% 4.43/2.45 thf(func_def_190, type, nu: variable > real).
% 4.43/2.45 thf(func_def_191, type, nu2: variable > real).
% 4.43/2.45 thf(func_def_192, type, omega: variable > real).
% 4.43/2.45 thf(func_def_193, type, omega2: variable > real).
% 4.43/2.45 thf(func_def_194, type, sigma: produc1418842292n_game).
% 4.43/2.45 thf(func_def_195, type, theta: trm).
% 4.43/2.45 thf(func_def_212, type, sK0: produc1699626005le_trm > produc1418842292n_game).
% 4.43/2.45 thf(func_def_213, type, sK1: produc1699626005le_trm > real).
% 4.43/2.45 thf(func_def_214, type, sK2: produc1699626005le_trm > set_variable).
% 4.43/2.45 thf(func_def_215, type, sK3: produc1699626005le_trm > char).
% 4.43/2.45 thf(func_def_216, type, sK4: produc1699626005le_trm > produc1418842292n_game).
% 4.43/2.45 thf(func_def_217, type, sK5: produc1699626005le_trm > set_variable).
% 4.43/2.45 thf(func_def_218, type, sK6: produc1699626005le_trm > trm).
% 4.43/2.45 thf(func_def_219, type, sK7: produc1699626005le_trm > char).
% 4.43/2.45 thf(func_def_220, type, sK8: produc1699626005le_trm > set_variable).
% 4.43/2.45 thf(func_def_221, type, sK9: produc1699626005le_trm > produc1418842292n_game).
% 4.43/2.45 thf(func_def_222, type, sK10: produc1699626005le_trm > trm).
% 4.43/2.45 thf(func_def_223, type, sK11: produc1699626005le_trm > trm).
% 4.43/2.45 thf(func_def_224, type, sK12: produc1699626005le_trm > set_variable).
% 4.43/2.45 thf(func_def_225, type, sK13: produc1699626005le_trm > produc1418842292n_game).
% 4.43/2.45 thf(func_def_226, type, sK14: produc1699626005le_trm > set_variable).
% 4.43/2.45 thf(func_def_227, type, sK15: produc1699626005le_trm > trm).
% 4.43/2.45 thf(func_def_228, type, sK16: produc1699626005le_trm > produc1418842292n_game).
% 4.43/2.45 thf(func_def_229, type, sK17: produc1699626005le_trm > produc1418842292n_game).
% 4.43/2.45 thf(func_def_230, type, sK18: produc1699626005le_trm > variable).
% 4.43/2.45 thf(func_def_231, type, sK19: produc1699626005le_trm > set_variable).
% 4.43/2.45 thf(func_def_232, type, sK20: produc1699626005le_trm > set_variable).
% 4.43/2.45 thf(func_def_233, type, sK21: produc1699626005le_trm > produc1418842292n_game).
% 4.43/2.45 thf(func_def_234, type, sK22: produc1699626005le_trm > trm).
% 4.43/2.45 thf(func_def_235, type, sK23: produc1699626005le_trm > trm).
% 4.43/2.45 thf(func_def_237, type, ph25: !>[X0: $tType]:(X0)).
% 4.43/2.45 thf(f959,plain,(
% 4.43/2.45 $false),
% 4.43/2.45 inference(trivial_inequality_removal,[status(thm)],[f958])).
% 4.43/2.45 thf(f958,plain,(
% 4.43/2.45 (none_fml != none_fml)),
% 4.43/2.45 inference(superposition,[status(thm)],[f943,f956])).
% 4.43/2.45 thf(f956,plain,(
% 4.43/2.45 ( ! [X0 : trm] : ((none_fml = (uSubst516392804stappf @ sigma @ ua @ (geq @ theta @ X0)))) )),
% 4.43/2.45 inference(equality_resolution,[status(thm)],[f953])).
% 4.43/2.45 thf(f953,plain,(
% 4.43/2.45 ( ! [X2 : trm,X3 : trm,X0 : set_variable,X1 : produc1418842292n_game] : (((uSubst516392818stappt @ sigma @ ua @ theta) != (uSubst516392818stappt @ X1 @ X0 @ X3)) | (none_fml = (uSubst516392804stappf @ X1 @ X0 @ (geq @ X3 @ X2)))) )),
% 4.43/2.45 inference(definition_unfolding,[status(thm)],[f933,f937])).
% 4.43/2.45 thf(f937,plain,(
% 4.43/2.45 (none_trm = (uSubst516392818stappt @ sigma @ ua @ theta))),
% 4.43/2.45 inference(cnf_transformation,[status(thm)],[f866])).
% 4.43/2.45 thf(f866,plain,(
% 4.43/2.45 (none_trm = (uSubst516392818stappt @ sigma @ ua @ theta))),
% 4.43/2.45 inference(flattening,[status(thm)],[f354])).
% 4.43/2.45 thf(f354,negated_conjecture,(
% 4.43/2.45 ~(none_trm != (uSubst516392818stappt @ sigma @ ua @ theta))),
% 4.43/2.45 inference(negated_conjecture,[status(cth)],[f353])).
% 4.43/2.45 thf(f353,conjecture,(
% 4.43/2.45 (none_trm != (uSubst516392818stappt @ sigma @ ua @ theta))),
% 4.43/2.45 file('/export/starexec/sandbox/tmp/tmp.Mj9VJvCut7/DTF2THF_26624.p',conj_0)).
% 4.43/2.45 thf(f933,plain,(
% 4.43/2.45 ( ! [X2 : trm,X3 : trm,X0 : set_variable,X1 : produc1418842292n_game] : ((none_fml = (uSubst516392804stappf @ X1 @ X0 @ (geq @ X3 @ X2))) | (none_trm != (uSubst516392818stappt @ X1 @ X0 @ X3))) )),
% 4.43/2.45 inference(cnf_transformation,[status(thm)],[f896])).
% 4.43/2.45 thf(f896,plain,(
% 4.43/2.45 ! [X0 : set_variable,X1 : produc1418842292n_game,X2 : trm,X3 : trm] : ((none_fml = (uSubst516392804stappf @ X1 @ X0 @ (geq @ X3 @ X2))) | ((none_trm != (uSubst516392818stappt @ X1 @ X0 @ X2)) & (none_trm != (uSubst516392818stappt @ X1 @ X0 @ X3))))),
% 4.43/2.45 inference(ennf_transformation,[status(thm)],[f876])).
% 4.43/2.45 thf(f876,plain,(
% 4.43/2.45 ! [X0 : set_variable,X1 : produc1418842292n_game,X2 : trm,X3 : trm] : ((none_fml != (uSubst516392804stappf @ X1 @ X0 @ (geq @ X3 @ X2))) => ((none_trm != (uSubst516392818stappt @ X1 @ X0 @ X2)) & (none_trm != (uSubst516392818stappt @ X1 @ X0 @ X3))))),
% 4.43/2.45 inference(rectify,[status(thm)],[f2])).
% 4.43/2.45 thf(f2,axiom,(
% 4.43/2.45 ! [X1 : set_variable,X0 : produc1418842292n_game,X3 : trm,X2 : trm] : (((uSubst516392804stappf @ X0 @ X1 @ (geq @ X2 @ X3)) != none_fml) => ((none_trm != (uSubst516392818stappt @ X0 @ X1 @ X3)) & ((uSubst516392818stappt @ X0 @ X1 @ X2) != none_trm)))),
% 4.43/2.45 file('/export/starexec/sandbox/tmp/tmp.Mj9VJvCut7/DTF2THF_26624.p',fact_1_usubstappf__geq__conv)).
% 4.43/2.45 thf(f943,plain,(
% 4.43/2.45 (none_fml != (uSubst516392804stappf @ sigma @ ua @ (geq @ theta @ eta)))),
% 4.43/2.45 inference(cnf_transformation,[status(thm)],[f3])).
% 4.43/2.45 thf(f3,axiom,(
% 4.43/2.45 (none_fml != (uSubst516392804stappf @ sigma @ ua @ (geq @ theta @ eta)))),
% 4.43/2.45 file('/export/starexec/sandbox/tmp/tmp.Mj9VJvCut7/DTF2THF_26624.p',fact_2_Geq_Oprems_I1_J)).
% 4.43/2.45 % SZS output end Proof for DTF2THF_26624
% 4.43/2.45 % (26752)------------------------------
% 4.43/2.45 % (26752)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.43/2.45 % (26752)Termination reason: Refutation
% 4.43/2.45
% 4.43/2.45 % (26752)Memory used [KB]: 7036
% 4.43/2.45 % (26752)Time elapsed: 0.052 s
% 4.43/2.45 % (26752)Instructions burned: 82 (million)
% 4.43/2.45 % (26752)------------------------------
% 4.43/2.45 % (26752)------------------------------
% 4.43/2.45 % (26722)Success in time 0.27 s
%------------------------------------------------------------------------------